MAT 151 - Basic Calculus with Applications

http://www.tiddlywiki.com/
http://www.giffmex.org/twfortherestofus.html

http://processing.tiddlyspot.com/
http://www.math.ist.utl.pt/~psoares/MathSVG.html

http://www.uncw.edu/reg/calendars-events.htm#Jun09

*Investigate how mathsvg and jsmath interact

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>

<<tabs practice
Practice "Practice" ./practice
Problems "Problems" ./practiceproblems
>>

<<tiddler [[LGR]]>>

<part LQ hidden>
Leading Question:  
An anthropologist would like to estimate the age of a subject using a measurement of deciduous molar crown length.  What is the maximum length expected?
</part>

<part data hidden>
Suppose that the length $L$ in millimeters is related to the number of weeks $t$ after conception by
$$L(t)=-0.01t^2 + 0.788t - 7.048.$$

[[Paper|resources/deciduous-molars.pdf]]
</part>

<part practice hidden>
</part>

<part practiceproblems hidden>
Find the absolute extrema if they exist, as well as all values of $x$ where they occur, for each function and specific domain.
# $f(x)=x^2+4x+5, -3 \le x \le 1$
# $f(x)=x^3+3x^2+1, -3 \le x \le 2$
# $f(x)=3x^5 - 5x^3, -2 \le x \le 0$
# $f(x)=\frac{x^2}{x-1}, -2 \le x \le -\frac{1}{2}$
# $f(x)=\frac{1}{x^2-9}, 0 \le x \le 2$
</part>

*The [[Learning Center]] is available to help you review course content.
*[[MyMathLab|resources/mml-handout-mat-151-012-2009-fall.pdf]] access is available for self-study.

<<tabs Examples
Set1 "Set1" ./antidiff1
Set2 "Set2" ./antidiff2
Set3 "Set3" ./antidiff3
Problem "Problem" ./antidiff4
>>
<part antidiff1 hidden>
Evaluate each indefinite integral.

# $\int 5 dx$
# $\int 5x^3 dx$
# $\int \root3{x} dx$
# $\int  4 \root5{x^4}dx$
# $\int \frac{1}{x^2} dx$

</part>
<part antidiff2 hidden>
Evaluate each indefinite integral.

# $\int -\frac{3}{x^3} dx$
# $\int \frac{1}{\sqrt{x}} dx$
# $\int \frac{2}{\root3{x^4}} dx$
# $\int 2x^3 -5x^2+4x-1 dx$
# $\int  x+3-\frac{3}{x^4}dx$
# $\int 3\sqrt{x}-\frac{1}{\root4{x^3}} dx$

</part>
<part antidiff3 hidden>
Evaluate each indefinite integral.

# $\int e^x dx$
# $\int e^{-x} dx$
# $\int e^{3x} dx$
# $\int \frac{4}{x} dx$
# $\int  e^x+3-\frac{2}{x} dx$
# $\int \frac{x^2-1}{x} dx$

</part>
<part antidiff4 hidden>
The slope of tangent line to a  curve $y=f(x)$ is given by
$$f'(x) = 6x^2-4x+3$$
If the curve passes through the point (0,1), find $f(x).$
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>

<<tabs Examples
Example "Example" ./example
Problem1 "Problem" ./optimization1
Problem2 "Problem" ./optimization2
Problem3 "Problem" ./optimization3
>>

<<tiddler [[LGR]]>>
<<tiddler [[HB]]>>

<part LQ hidden>
Leading Question:  
How should cans be designed to minimize the material needed to construct them or to maximize the volume?
</part>

<part data hidden>
Recall that the volume of a cylindrical can of radius $r$ and height $h$ is given by $\pi r^2 h,$ and that the lateral area is given by $2 \pi r h.$
</part>

<part example hidden>
</part>

<part optimization1 hidden>
A cylindrical can is to be constructed to hold a fixed volume of liquid.  The cost of the material used for the top and bottom of the can is 3 cents per square inch, and the cost of the materials used for the curved side is 2 cents per square inch.  Use calculus to find a simple relationship between the radius and height of the can that is the least costly to construct.
</part>

<part optimization2 hidden>
The highway department is planning to build a picnic park for motorists along a major highway.  The park is to be rectangular with an area of 5,000 square yards and is to be fenced off on the three sides not adjacent to the highway.  What is the least amount of fencing required for this job?  How long and wide should the park be for the fencing to be minimized?
</part>


<part optimization3 hidden>
A cable is to be run from a power plant on one side of a river 900 meters wide to a factory on the other side, 3,000 meters downstream.  The cost of running the cable under the water is 5 dollars per meter, while the cost over land is 4 dollars per meter.  What is the most economical route over which to run the cable?
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>

<part LQ hidden>
Leading Question:  
What interest rate will cause 5000 dollars to grow to 7250 dollars in 4 years if interest is compounded continuously?
</part>

<part data hidden>
We must use the continuous compounding formula.
</part>

Type the text for 'New Tiddler'

[[Maple Worksheet|http://people.uncw.edu/freezem/math161/lectures/maple/c5s2ver1.mws]]

An array is a list of data. Each piece of data in an array is identified by an index number representing its position in the array. Arrays are zero based, which means that the first element in the array is [0], the second element is [1], and so on. In this example, an array named "coswav" is created and filled with the cosine values. This data is displayed three separate ways on the screen.

<<Processing 

size(200, 200);

float[] coswave = new float[width];

for(int i=0; i<width; i++) {
  float ratio = (float)i/(float)width;
  coswave[i] = abs( cos(ratio*PI) );
}

for(int i=0; i<width; i++) {
  stroke(coswave[i]*255);
  line(i, 0, i, width/3);
}

for(int i=0; i<width; i++) {
  stroke(coswave[i]*255/4);
  line(i, width/3, i, width/3*2);
}

for(int i=0; i<width; i++) {
  stroke(255-coswave[i]*255);
  line(i, width/3*2, i, height);
}

>>

Taken from [[basic/array.html|http://ejohn.org/apps/processing.js/examples/basic/array.html]]

Please refresh/reload the webpage to see the latest updates.
<<tabs Assignments
Quizzes "Quizzes" [[Quizzes]]
Tests "Tests" [[Tests]]
Homework "Homework" [[Homework]]
>>

*Instructor
**Dr. Michael Freeze
*Class meeting time
**Section 012:  Tuesdays and Thursdays, 09:30-10:45a in Bear 206
*Office Location
**Bear Hall 124
*Office Hours
**by appointment
*Phone
**910.795.1385
*Email
**freezem at uncw dot edu

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
How does the average cost per day of a rental car change with the number of days the car is rented?
</part>

<part data hidden>
Suppose that a car rental firm charged 36 dollars per day or portion of a day to rent a car for a period of 1 to 5 days.  Days 6 and 7 were then free, while the charge for days 8 through 12 was again 36 dollars per day.
</part>

All shapes drawn to the screen have a position that is specified as a coordinate. All coordinates are measured as the distance from the origin in units of pixels. The origin [0, 0] is the coordinate is in the upper left of the window and the coordinate in the lower right is [width-1, height-1].

<<Processing 

// Sets the screen to be 200, 200, so the width of the window is 200 pixels
// and the height of the window is 200 pixels
size(200, 200);
background(0);
noFill();
stroke(255);

// The two parameters of the point() method each specify coordinates.
// This call to point() draws at the position [100, 100]
point(width/2, height/2);

// Draws to the position [100, 50]
point(width/2, height/4); 

// It is also possible to specify a point with any parameter, 
// but only coordinates on the screen are visible
point(60, 30);
point(60, 134);
point(160, 50);
point(280, -800);
point(201, 100);

// Coordinates are used for drawing all shapes, not just points.
// Parameters for different methods are used for different purposes.
// For example, the first two parameters to line() specify the coordinates of the 
// first point and the second two parameters specify the second point
stroke(204);
line(0, 73, width, 73);

// The first two parameters to rect() are coordinates
// and the second two are the width and height
rect(110, 55, 40, 36);

>>

Taken from [[basic/coordinates.html|http://ejohn.org/apps/processing.js/examples/basic/coordinates.html]]

!Objectives
#To provide students with a working knowledge of the fundamental concepts and techniques of differential and integral calculus of algebraic functions of one variable.
#To provide students experience with application of calculus techniques and use of technology in solving problems concerning rates of change.
#To emphasize algebraic, numeric, geometric, and verbal approaches to calculus concepts.
!Text
//Calculus with Applications, 9th edition//, Lial, Greenwell, and Ritchey.
!Calculator
A TI 83/84+ graphing calculator is strongly recommended for this course.			
!Attendance
You are expected to attend class on time each day. Attendance will be recorded on a regular basis.		
!Tests, Homework, and Quizzes
Two tests and a final exam will be given. There will be no make-up tests without prior permission. Homework problems will be suggested for each section. Short unannounced quizzes may also be given occasionally.
!Grading
Each of your two tests will contribute 30% toward your grade. Your combined homework and quiz grades will contribute an additional 10%, and your final exam will determine the remaining 30%.
/%
!Plus/Minus Modifiers
A plus or minus may be used as a possible grade modifier, for final grades only, at the end of the semester.  Factors that influence the judgment to assign a + or – (or neither) are:  performance on the final exam, consistency of performance throughout the semester, proximity to a grade borderline, class participation and effort.
%/
!Incompletes
A grade of I (incomplete) is given only if documented circumstances beyond the student’s control (e.g., medical, legal) render the student unable to complete the course work, and only if there is a reasonable possibility of passing the course. The grade I is not given for simply failing to meet the course requirements.
!Academic Expectations
In choosing UNCW, you have become part of our community of scholars.  We recognize that the UNCW learning experience is challenging and requires hard work.  It also requires a commitment to make time available to do that hard work.  The university expects you to make academics your highest priority by dedicating your time and energy to training your mind and acquiring knowledge.

You are expected to follow the academic Honor Code as covered in the UNCW Student Handbook.  Please note that plagiarism, a form of academic dishonesty in which you take someone else's ideas and represent them as your own, is a specific violation of the Honor Code.

Academic success in critical thinking and problem solving prepares you for the changes and challenges you will encounter in the future.  Our faculty and academic support resources are readily available as partners in this effort, but the primary responsibility for learning is yours.
!Federal Americans with Disabilities Act
Students with diagnosed disabilities should contact the Office of Disability Services.  Please give me, within the first week of class or as soon as possible, a copy of the letter you receive from Office of Disability Services detailing class accommodations you may need.  If you require accommodation for test-taking please make sure I have the referral letter no less than three days before the test.
!Violence and Harassment
UNCW practices a zero tolerance policy for any kind of violent or harassing behavior.  If you are experiencing an emergency of this type contact the police at 911 or UNCW CARE at 962-2273.  Resources for individuals concerned with a violent or harassing situation can be located at http://www.uncw.edu/wsrc/crisis.html.
!Campus Respect Compact
UNCW has recently instituted a Respect Compact to affirm our commitment to a civil community characterized by mutual respect.  A copy of the Respect Compact is affixed to the wall of each classroom and can be accessed at http://www.uncw.edu/stuaff/pdc/documents/SeahawkRespectCompact.pdf .  Individuals desiring more information about the Respect Compact should contact the Office of Institutional Diversity and Inclusion.

Graph each function, considering the domain, critical points, symmetry, regions where the function is increasing or decreasing, inflection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable.

# $f(x) = x^5 - 15x^3$
# $f(x) = \frac{3x}{x-2}$
# $f(x) = \frac{1}{x^2-9}$
# $f(x) = x e^{-x}$

[[Announcements]]
[[Schedule]]

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
How does the risk of chromosomal abnormality in a child change with the mother's age?
</part>

<part data hidden>
See graph in Example 3 of Section 3.4.
</part>

{{center{
Secant line of $\left\{\begin{array}{l l}
x^2, & \textrm{if } x < 1 \\
x^2+1, & \textrm{if } x \ge 1
\end{array}\right.$  at $a=1$
}}}
(:graph(center,{width:250,height:250,scales:[-2.5,2.5,-0.7,3]})
dynamic.click = function() {
  a=SVG.mouse[0];
  fa2 = f2(a);
  setOptions({stroke:"blue",markerstroke:"blue"});
  line([a,fa2],[a,0],{id:"apos",marker:"*-*",label:["P","a"],pos:["w","n"],strokedasharray: "10,10"});
  m = (f2(a+0.01)-fa2)/0.01;
  c = fa2-m*a;
  if (a!=1) plot("m*x+c",{min:-2.5,max:2.5,id:"tangent",points:2,strokedasharray:"none", stroke:"red", strokewidth:2});
};

dynamic.update = function() {
  fb2 = f2(b);
  setOptions({stroke: "green",markerstroke: "green"});
  line([b,fb2],[b,0],{id:"xpos",marker:"*-*",label:["Q","x"],pos:["e","n"],strokedasharray: "10,10"});
  if (abs(b-a)>0.000001) m = (fb2-fa2)/(b-a);
  else m = (f2(a+0.01)-fa2)/0.01;
  c = fa2-m*a;
  plot("m*x+c",{min:-2.5,max:2.5,id:"secant",points:2,strokedasharray:"none", strokewidth:2});
  text([-2.5,-0.6],"slope = "+m.toFixed(2),{pos:"ne",id:"slope"});
  b = SVG.mouse[0];
};

axes();
setAction("mousemove",dynamic.update);
setAction("click",dynamic.click);
f2=function(x){return (x < 1?x*x:x*x+1)};
plot(f2,{steps:[1],leftMarkers:"o",rightMarkers:"*"});
a = 1;
b = 0.8;
dynamic.click();
dynamic.update();
:)

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
Given a new product whose rate of growth is rapid at first and then slows, how can we find the rate of growth?
</part>

<part data hidden>
Suppose the sales of the product as a function of time is
$$S(t) = \frac{100000}{1 + 100 e^{-0.3t} },$$
where $t$ is measured in years.
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
How does the average velocity of pedestrians in a city vary with the population size?
</part>

<part data hidden>
Model the average speed of pedestrians by
$$f(x) = 0.873 \log(x) - 0.0255,$$
where $x$ is the city population size.
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
A manufacturer of small motors wants to make the average cost per motor as small as possible.  How can this be done?
</part>

<part data hidden>
Suppose the cost in dollars of manufacturing $x$ hundred small motors is given by
$$C(x) = \frac{3x^2+120}{2x+1}, 10 \le x \le 200.$$
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>

<part LQ hidden>
Leading Questions:
How much interest will an investment earn?  

What is the oxygen consumption of yearling salmon?
</part>

<part data hidden>
With compound interest, the value of an investment increases exponentially over time.

Biologists studying salmon have found that the oxygen consumption of yearling salmon increases exponentially with the speed of swimming.
</part>

/***
|Name|ExternalTiddlersPlugin|
|Source|http://www.TiddlyTools.com/#ExternalTiddlersPlugin|
|Documentation|http://www.TiddlyTools.com/#ExternalTiddlersPluginInfo|
|Version|1.3.1|
|Author|Eric Shulman|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|plugin|
|Requires|TemporaryTiddlersPlugin (optional, recommended)|
|Overrides|config.macros.tiddler.handler|
|Options|##Configuration|
|Description|retrieve and wikify content from external files or remote URLs|
This plugin extends the {{{<<tiddler>>}}} macro syntax so you can retrieve and wikify content directly from external files or remote URLs.  You can also define alternative "fallback" sources to provide basic "import on demand" handling by automatically creating/importing tiddler content from external sources when the specified ~TiddlerName does not already exist in your document.
!!!!!Documentation
>see [[ExternalTiddlersPluginInfo]]
!!!!!Configuration
<<<
<<option chkExternalTiddlersImport>> automatically create/import tiddlers when using external fallback references
{{{usage: <<option chkExternalTiddlersImport>>}}}
<<option chkExternalTiddlersQuiet>> don't display messages when adding tiddlers ("quiet mode")
{{{usage: <<option chkExternalTiddlersQuiet>>}}}
<<option chkExternalTiddlersTemporary>> tag retrieved tiddlers as 'temporary'(requires [[TemporaryTiddlersPlugin]])
{{{usage: <<option chkExternalTiddlersTemporary>>}}}
tag retrieved tiddlers with: <<option txtExternalTiddlersTags>>
{{{usage: <<option txtExternalTiddlersTags>>}}}

__password-protected server settings //(optional, if needed)//:__
>username: <<option txtRemoteUsername>> password: <<option txtRemotePassword>>
>{{{usage: <<option txtRemoteUsername>> <<option txtRemotePassword>>}}}
>''note: these settings are also used by [[LoadTiddlersPlugin]] and [[ImportTiddlersPlugin]]''
<<<
!!!!!Revisions
<<<
2008.10.27 [1.3.1] in insertTiddler(), fixed Safari bug by replacing static Array.concat(...) with new Array().concat(...)
|please see [[ExternalTiddlersPluginInfo]] for additional revision details|
2007.11.25 [1.0.0] initial release - moved from CoreTweaks
<<<
!!!!!Code
***/
//{{{
version.extensions.ExternalTiddlersPlugin= {major: 1, minor: 3, revision: 1, date: new Date(2008,10,27)};

// optional automatic import/create for missing tiddlers
if (config.options.chkExternalTiddlersImport==undefined) config.options.chkExternalTiddlersImport=true;
if (config.options.chkExternalTiddlersTemporary==undefined) config.options.chkExternalTiddlersTemporary=true;
if (config.options.chkExternalTiddlersQuiet==undefined) config.options.chkExternalTiddlersQuiet=false;
if (config.options.txtExternalTiddlersTags==undefined) config.options.txtExternalTiddlersTags="external";
if (config.options.txtRemoteUsername==undefined) config.options.txtRemoteUsername="";
if (config.options.txtRemotePassword==undefined) config.options.txtRemotePassword="";

config.macros.tiddler.externalTiddlers_handler = config.macros.tiddler.handler;
config.macros.tiddler.handler = function(place,macroName,params,wikifier,paramString,tiddler)
{
	params = paramString.parseParams("name",null,true,false,true);
	var names = params[0]["name"];
	var list = names[0];
	var items = list.split("|"); 
	var className = names[1] ? names[1] : null;
	var args = params[0]["with"];

	// UTILITY FUNCTIONS
	function extract(text,tids) { // get tiddler source content from plain text or TW doc
		if (!text || !tids || !tids.length) return text; // no text or no tiddler list... return text as-is
		var remoteStore=new TiddlyWiki();
		if (!remoteStore.importTiddlyWiki(text)) return text; // not a TW document... return text as-is
		var out=[]; for (var t=0;t<tids.length;t++)
			{ var txt=remoteStore.getTiddlerText(tids[t]); if (txt) out.push(txt); }
		return out.join("\n");
	}
	function substitute(text,args) { // replace "substitution markers" ($1-$9) with macro param values (if any)
		if (!text || !args || !args.length) return text;
		var n=args.length; if (n>9) n=9;
		for(var i=0; i<n; i++) { var re=new RegExp("\\$" + (i + 1),"mg"); text=text.replace(re,args[i]); }
		return text;
	}
	function addTiddler(src,text,tids) { // extract tiddler(s) from text and create local copy
		if (!config.options.chkExternalTiddlersImport) return; // not enabled... do nothing
		if (!text || !tids || !tids.length) return; // no text or no tiddler list... do nothing
		var remoteStore=new TiddlyWiki();
		if (!remoteStore.importTiddlyWiki(text)) // not a TW document... create a single tiddler from text
			makeTiddler(src,text,tids[0]);
		else // TW document with "permaview-like" suffix... copy tiddler(s) from remote store
			for (var t=0;t<tids.length;t++)
				insertTiddler(src,remoteStore.getTiddler(tids[t]));
		return;
	}
	function makeTiddler(src,text,title) { // create a new tiddler object from text
		var who=config.options.txtUserName; var when=new Date();
		var msg="/%\n\nThis tiddler was automatically created using ExternalTiddlersPlugin\n";
		msg+="by %0 on %1\nsource: %2\n\n%/";
		var tags=config.options.txtExternalTiddlersTags.readBracketedList();
		if (config.options.chkExternalTiddlersTemporary) tags.pushUnique(config.options.txtTemporaryTag); 
		store.saveTiddler(null,title,msg.format([who,when,src])+text,who,when,tags,{});
		if (!config.options.chkExternalTiddlersQuiet) displayMessage("Created new tiddler '"+title+"' from text file "+src);
	}
	function insertTiddler(src,t) { // import a single tiddler object into the current document store
		if (!t) return;
		var who=config.options.txtUserName; var when=new Date();
		var msg="/%\n\nThis tiddler was automatically imported using ExternalTiddlersPlugin\n";
		msg+="by %0 on %1\nsource: %2\n\n%/";
		var newtags=new Array().concat(t.tags,config.options.txtExternalTiddlersTags.readBracketedList());
		if (config.options.chkExternalTiddlersTemporary) newtags.push(config.options.txtTemporaryTag);
		store.saveTiddler(null,t.title,msg.format([who,when,src])+t.text,t.modifier,t.modified,newtags,t.fields);
		if (!config.options.chkExternalTiddlersQuiet) displayMessage("Imported tiddler '"+t.title+"' from "+src);
	}
	function getGUID()  // create a Globally Unique ID (for async reference to DOM elements)
		 { return new Date().getTime()+Math.random().toString(); }

	// loop through "|"-separated list of alternative tiddler/file/URL references until successful
	var fallback="";
	for (var i=0; i<items.length; i++) { var src=items[i];
		// if tiddler (or shadow) exists, replace reference list with current source name and apply core handler
		if (store.getTiddlerText(src)) {
			arguments[2][0]=src; // params[] array
			var p=arguments[4].split(list); arguments[4]=p[0]+src+p[1]; // paramString
			this.externalTiddlers_handler.apply(this,arguments);
			break; // stop processing alternatives
		}
		// tiddler doesn't exist, and not an external file/URL reference... skip it
		if (!config.formatterHelpers.isExternalLink(src)) {
			if (!fallback.length) fallback=src; // title to use when importing external tiddler
			continue;
		}
		// separate 'permaview' list of tiddlers (if any) from file/URL (i.e., '#name name name..." suffix)
		var p=src.split("#"); src=p[0]; var tids=p[1]?p[1].readBracketedList(false):[];
		// if reference is to a remotely hosted document or the current document is remotely hosted...
		if (src.substr(0,4)=="http" || document.location.protocol.substr(0,4)=="http") {
			if (src.substr(0,4)!="http") // fixup URL for relative remote references
				{ var h=document.location.href; src=h.substr(0,h.lastIndexOf("/")+1)+src; }
			var wrapper = createTiddlyElement(place,"span",getGUID(),className); // create placeholder for async rendering
			var callback=function(success,params,text,src,xhr) { // ASYNC CALLBACK
				if (!success) { displayMessage(xhr.status); return; } // couldn't read remote file... report the error 
				if (params.fallback.length)
					addTiddler(params.url,text,params.tids.length?params.tids:[params.fallback]); // import tiddler
				var wrapper=document.getElementById(params.id); if (!wrapper) return; 
				wikify(substitute(extract(text,params.tids),params.args),wrapper); // ASYNC RENDER
			};
			var callbackparams={ url:src, id:wrapper.id, args:args, tids:tids, fallback:fallback }  // ASYNC PARAMS
			var name=config.options.txtRemoteUsername; // optional value
			var pass=config.options.txtRemotePassword; // optional value
			var x=doHttp("GET",src,null,null,name,pass,callback,callbackparams,null)
			if (typeof(x)=="string") // couldn't start XMLHttpRequest... report error
				{ displayMessage("error: cannot access "+src); displayMessage(x); }
			break; // can't tell if async read will succeed.... stop processing alternatives anyway.
		}
		else { // read file from local filesystem
			var text=loadFile(getLocalPath(src));
			if (!text) { // couldn't load file... fixup path for relative reference and retry...
				var h=document.location.href;
				var text=loadFile(getLocalPath(decodeURIComponent(h.substr(0,h.lastIndexOf("/")+1)))+src);
			}
			if (text) { // test it again... if file was loaded OK, render it in a class wrapper
				if (fallback.length) // create new tiddler using primary source name (if any)
					addTiddler(src,text,tids.length?tids:[fallback]);
				var wrapper=createTiddlyElement(place,"span",null,className);
				wikify(substitute(extract(text,tids),args),wrapper); // render
				break; // stop processing alternatives
			}
		}
	}
};
//}}}

|Name|ExternalTiddlersPluginInfo|
|Source|http://www.TiddlyTools.com/#ExternalTiddlersPlugin|
|Documentation|http://www.TiddlyTools.com/#ExternalTiddlersPluginInfo|
|Version|1.3.1|
|Author|Eric Shulman|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|documentation|
|Requires||
|Overrides||
|Description|documentation for ExternalTiddlersPlugin|
This plugin extends the {{{<<tiddler>>}}} macro syntax so you can retrieve and wikify content directly from external files or remote URLs.  You can also define alternative "fallback" sources to provide basic "import on demand" handling by automatically creating/importing tiddler content from external sources when the specified ~TiddlerName does not already exist in your document.
!!!!!Configuration
>see ExternalTiddlersPlugin
!!!!!Usage
<<<
The standard TiddlyWiki core syntax for the {{{<<tiddler>>}}} macro is:
>{{{<<tiddler TiddlerName with: param param param ...>>}}}
where the optional {{{with: param param param...}}} values are used to replace any corresponding "substitution markers" ($1 to $9) that may be embedded in the referenced tiddler content.

This plugin allows the {{{<<tiddler>>}}} macro to ''use external file/URL references in place of the usual ~TiddlerName parameter'', so that you can render wiki-formatted source content retrieved from an external file/URL reference (as determined by the core's isExternalLink() test function), ''//as if// it had come from a tiddler in the current document''.  The external file/URL can be either ''a relative or absolute reference'' and can contain ''"plain text" or a full TiddlyWiki document''.  When using a TiddlyWiki document, you must specify which tiddlers should be included in the output by appending a permaview-like suffix to the file or URL reference, e.g.:
>{{{<<tiddler "myfile.txt" with: param param param...>>}}}
>or
>{{{<<tiddler "myfile.html#TiddlerName TiddlerName..." with: param param param...>>}}}
>or
>{{{<<tiddler "http://www.TiddlyWiki.com/index.html#HelloThere" with: param param param...>>}}}
If the plugin-enhanced {{{<<tiddler>>}}} macro is unable to retrieve the external content --  perhaps because the file doesn't exist or doesn't contain the requested tiddler(s), or cross-domain security blocked file access, or the network/server "timed out", etc., -- then it produces no output (i.e., just as when the standard {{{<<tiddler>>}}} macro is given a ~TiddlerName does not exist in the current document.)
<<<
!!!!!Using alternative "fallback" references
<<<
In addition to using external file/URL references in place of the usual ~TiddlerName, the plugin also allows you to use a ''fallback list'' consisting of a combination of alternative sources: tiddlers, local files, and/or URL references, each separated by "|".  The first reference in a fallback list is the "primary source"; the remaining references are "fallback sources".  The plugin will attempt to retrieve content from each fallback source until one is successfully retrieved or all alternatives have been tried.

For example, if you create a tiddler called [[HelloThere]], as well as a remotely-hosted TW document containing a published tiddler, also called [[HelloThere]], then you can write:
>{{{<<tiddler [[HelloThere|http://www.TiddlyWiki.com/#HelloThere]]>>}}}
When [[HelloThere]] is present in the local document, it is processed in the normal manner.  However, if you delete the  local [[HelloThere]] tiddler, the plugin will attempt to retrieve the [[HelloThere]] tiddler from the indicated remote URL.

Please note: although you can list any number of alternative sources, in whatever order you prefer, retrieval from a remote URL occurs asynchronously via XMLHttpRequest() processing.  As a consequence, there can be ''no more than one remote URL reference in the fallback list'', and any alternatives that follow a remote URL reference will not be processed.
<<<
!!!!!Automatically import/create missing tiddlers
<<<
When content is retrieved from an external fallback source, the plugin can automatically import/create tiddler(s) containing that content into your document, allowing you to display, modify, save and/or search for text in that tiddler from within your own document, without needing to retrieve it again from the external source.

If no local ~TiddlerName(s) are specified in the fallback list (i.e., only direct file/URL references are present), then a tiddler will NOT be created, so that each time you render the tiddler display the external source will be re-read in order to render the most recently saved external file content.  To illustrate using the example from above:
>&nbsp;&nbsp;&nbsp;{{{<<tiddler [[HelloThere|http://www.TiddlyWiki.com/#HelloThere]]>>}}}
will automatically create a locally-stored [[HelloThere]] tiddler, so that the external source is only accessed the first time the content is rendered, while:
>&nbsp;&nbsp;&nbsp;{{{<<tiddler [[http://www.TiddlyWiki.com/#HelloThere]]>>}}}
will re-load the content from the external source each time the display is rendered.

For easy identification, any tiddlers that are automatically created/imported are tagged with <<tag external>> (or other custom-defined tag values).  These tiddlers can also be automatically tagged with <<tag temporary>> for use with [[TemporaryTiddlersPlugin]], which will skip over those tiddlers when saving changes to your document so that when you reload the document, the temporary tiddlers will no longer be present and will be retrieved anew from the external source, on demand, when (or if) they are needed.  Important reminder: ''If you modify a temporary tiddler and want to retain it in your local document, be sure to remove the <<tag temporary>> tag from the tiddler before saving.''
<<<
!!!!!~XMLHttpRequest: performance and security issues
<<<
This plugin uses asynchronous XMLHttpRequest() processing to access external content directly from URLs hosted on remote web servers.  This often creates delays ranging from mere moments to many minutes while waiting for the remote web server to transfer the requested file.  This performance can vary greatly depending upon the size of the remote file, how the remote server responds to repeated requests for the same URL (e.g, with a //"304 - no change"// response code), as well as how your ''browser's cache mechanism'' has been configured (to avoid repeated downloads).

In addition to server-originated delays, ''cross-domain access from one remote domain to another using XMLHttpRequest() processing is generally restricted for security reasons''.  As a result, if you publish your document to a remote web server, then external file/URL references contained in that document will not work if they are not located on the same server as the hosted document.

Fortunately, this security restriction does NOT usually apply when accessing remote URLs rendered into a locally-viewed document, since blocking such access would interfere with normal browser functions!  As a "rule of thumb", in order to ensure that external content included in server-hosted documents will be displayed as intended, you should ''always use either a relative path/file reference or an http: reference located on the same domain as the published document.'' for any document you intend to publish.

Note: Some hosting providers, such as http://www.TiddlySpot.com/ offer ''"proxy" services that may allow you to bypass the security restrictions'' for certain designated remote web sites.  Consult your hosting service for information regarding their proxy arrangments (if any).
<<<
!!!!!Revisions
<<<
2008.10.27 [1.3.1] in insertTiddler(), fixed Safari bug by replacing static Array.concat(...) with new Array().concat(...)
2008.01.08 [*.*.*] plugin size reduction: documentation moved to ExternalTiddlersPluginInfo
2008.01.03 [1.3.0] use lower-level doHttp() instead loadRemoteFile() so that optional username/password values can be used in XMLHttpRequest
2007.12.22 [1.2.2] in handler(), when reading from local file with relative path fixup, use decodeURIComponent() instead of decodeURI 
2007.11.30 [1.2.1] lots of code/docmentation cleanup.  renamed option cookies.  changed auto tag value to "external".
2007.11.27 [1.2.0] added support for automatically importing external tiddlers
2007.11.26 [1.1.1] improved XMLHttpRequest() error reporting for cross-domain security issues
2007.11.26 [1.1.0] added support for multiple alternative fallback references
2007.11.25 [1.0.0] initial release - moved from CoreTweaks
<<<

(:graph(center,{width:200,height:200,scales:[-1.1,1.1],coords: 'none'})
a = []
n = 9
 for (i = 0; i < n; i++)
 a[i] = [cos(PI/4*(-1)*i+PI/2),
 sin(PI/4*(-1)*i+PI/2)]
path([a[0],a[3],a[6],a[1],a[4],a[7],a[2],a[5],
 a[0],a[4],a[5],a[1],a[2],a[6],a[7],a[3]])
path(a,{marker:"oo",markerfill:"orange"})
:)
(:graph({width:250,height:250,scales:[-10,10]})
axes({dx:2});
polarPlot("x/PI",{min:0,max:10*PI,stroke:"red"});
:)

A famous result due to [[Euler|http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html]] in ~LaTeX: $\sum_{n=1}^{+\infty}{\frac1{n^2}=\frac{\pi^2}6$
and again as a centered equation using {{{$$ ... $$}}}$$\sum_{n=1}^{+\infty} \frac{1}{n^2}=\frac{\pi^2}{6}.$$
or using {{{\[ ... \]}}} \[\sum_{n=1}^{+\infty} \frac{1}{n^2}=\frac{\pi^2}{6}.\]
Here is a graph of $x-\frac{x^3}{6}$ and $\sin(x)$

(:graph({width:600,height:300,scales:[-6.29,6.29]})
grid({dx:1,stroke:"green"});
axes({marker:">"});
plot("sin(x)",{stroke:"red"})
plot("x-pow(x,3)/6",{min:-4,max:4,stroke:"blue", strokedasharray:"10,10"})
text([-2,-2.5],"Close friends near 0!",{id:"rot",fontsize:18,fill:"orange"});
rotate("rot",PI/18,{center:[-5,-3]});
:)
and a diagram illustrating why Pythagoras' Theorem holds:

(:graph({width:400,height:150,scales:[-4,4,1,4],coords:"none"})
setOptions({fill:"yellow"});
rect([1,1],[4,4])
rect([-4,1],[-1,4])
setOptions({fill:"red"});
rect([-2,1],[-1,2])
setOptions({fill:"blue"});
rect([-4,2],[-2,4])
setOptions({fill:"green"});
path([[1,2],[2,4],[4,3],[3,1],[1,2]])
setOptions({fill:"none"});
path([[-4,1],[-2,2],[-1,4]])
:)

<<tabs Examples
Strategy "Strategy" ./strategy
Problem1 "Problem" ./optimization1
Problem2 "Problem" ./optimization2
Problem3 "Problem" ./optimization3
Problem4 "Problem" ./optimization4
Problem5 "Problem" ./optimization5
>>

<<tiddler [[LGR]]>>
<<tiddler [[HB]]>>

<part strategy hidden>
Solving an Applied Extrema Problem

#Read the problem carefully. Make sure you understand what is given and what is unknown.
#If possible, sketch a diagram. Label the various parts.
#Decide on the objective variable that must be maximized or minimized. Express that variable as a function of //one// other variable.
#Find the domain of the function.
#Find the critical numbers for the objective function.
#If the domain is a closed interval, evaluate the function at the endpoints and at each critical number to see which yields the absolute maximum or minimum. If the domain is an open interval, apply the critical point theorem when there is only one critical number. If there is more than one critical number, evaluate the function at the critical numbers and also find the limit as the endpoints of the interval are approached to determine if an absolute maximum or minimum exists at one of the critical numbers.
</part>

<part optimization1 hidden>
A manufacturer can produce blank videodiscs at a cost of 2 dollars apiece. The videodiscs have been selling for 5 dollars apiece, and at this price, consumers have been buying 4,000 videodiscs a month. The manufacturer is planning to raise the price of the videodiscs and estimates that for each 1 dollar increase in the price, 400 fewer videodiscs will be sold each month. At what price should the manufacturer sell the videodiscs to maximize profit?
</part>

<part optimization2 hidden>
A 300 room hotel in Las Vegas is filled to capacity every night at 80 dollars per room. For each 1 dollar increase in room rate, 3 fewer rooms are occupied. If each occupied room costs 10 dollars to service per day, how much should hotel management charge for each room to maximize daily profit?
</part>

<part optimization3 hidden>
A publishing company sells 25,000 copies of a certain book each year. Storage costs, based on the average number of books in the warehouse, are 1 dollar per book per year. Each time the company must print additional copies, it costs the company 1,000 dollars to set up the presses each time it prints a batch of books. How many books should the company produce during each printing in order to minimize its total storage and setup costs?
</part>

<part optimization4 hidden>
A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular open box. What size square should be cut from each corner to obtain a maximum volume?
</part>

<part optimization5 hidden>
A freshwater pipe is to be run from a source on the edge of a lake to a small resort community on an island 5 miles offshore using two straight-line paths. The distance from the source to the nearest point on the lake edge to the island is 10 miles. If it costs 1.5 times as much to lay the pipe in the lake as it does on land, what should the length of the pipe on land be to minimize the total cost of the project?
</part>

(:graph({width:120,height:120,scales:[-0.5,1.5,-0.5,1.5],coords:"none"})
a=[0,1];
b=[1,1];
c=[1,0];
d=[0,0];
path([b,d,a,c]);
path([a,b,c,d],{marker:"ooo",markerfill:"yellow",label:["a","b","c","d"],pos:["nw","ne","se","sw"]});
text([.5,-0.5],"$K_4$",{pos:"n"})
:)

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>

[[xfunctions applet|resources/xfunctions.html]]

<part LQ hidden>
Leading Question:  
Given a graph of the cost function, how can we find the graph of the marginal cost function?
</part>

<part data hidden>
Consider the DVD cost function $C(x)=100+15x-x^2, 0 \le x \le 7$ and the taco cost function $C(x)= - 0.00375x^2+1.5x+1000, 0 \le x \le 180.$
</part>

from //Calculus, 8th edition//, by Hoffman and Bradley

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
Just because the price of a stock is increasing, does that alone make it a good investment?
</part>

<part data hidden>
Model the price of a company's stock by
$$P(t) = 17 + t^{1/2},$$
where $t$ is the number of months since the stock became available.
</part>

<<tiddler [[LGR]]>>

| Section 1.1 |1-59 odd,61,65,69,73 |
| Section 1.2 |1-25 odd,27,29,33,37,43 |
| Section 2.1 |1-73 odd,75,79,83 |
| Section 2.2 |1-43 odd,45,51,55,59,63 |
| Section 2.3 |1-45 odd,47,49,53,59,61,63 |
| Section 2.4 |1-31 odd,33,37,45,47 |
| Section 2.5 |1-65 odd,67,69,73,75,81 |
| Section 2.6 |1,3,7,11,15,31,35,39 |
| Section 3.1 |1-77 odd,79,81,87 |
| Section 3.2 |1-33 odd,35,37,39 |
| Section 3.3 |1-23 odd,27,29,35,39,41 |
| Section 3.4 |1-45 odd,49,53,57 |
| Section 3.5 |1-15 odd |
| Section 4.1 |1-47 odd |
| Section 4.2 |1-37 odd,39,45,47,51 |
| Section 4.3 |1-41 odd,55,59,61 |
| Section 4.4 |1-33 odd,37,45,49,57,61 |
| Section 4.5 |1-43 odd,55,59,63,65 |
| Section 5.1 |1-35 odd,47,51,55 |
| Section 5.2 |1-33 odd,43,51,55 |
| Section 5.3 |1-47 odd,71,73,81,93 |
| Section 5.4 |1-39 odd |
| Section 6.1 |1-37 odd,41,51,55 |
| Section 6.2 |1,3,5,7,9,11,13,17,23,33 |
| Section 6.3 |5,7,9,11,15,21,23 |
| Section 6.4 |1-37 odd,43,45,47 |
| Section 6.5 |1-7 odd,9,11,15,17,21,23,27 |
| Section 7.1 |1-55 odd,61,63,65,67 |
| Section 7.2 |1-35 odd,39,41 |
| Section 7.3 |1-23 odd,25,29,35 |
| Section 7.4 |1-43 odd,55,57,65,69,71 |
| Section 7.5 |1-25 odd,31,33,39 |
| Section 7.6 |1-13 odd,21,23,31 |

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
How can one determine the slope of a curve which is defined by an equation in more than one variable?
</part>

<part data hidden>

</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
How long is it profitable to increase production?
</part>

<part data hidden>
Suppose that the the cost in dollars of producing $x$ units, for $0 \le x \le 1000,$ is
$$C(x) = 1000x - 0.2x^2,$$
and the revenue can be approximated by
$$R(x) = 0.0008x^3 - 2.4x^2 + 2400x.$$
</part>

from //Calculus with Applications, 9th edition//, Lial, Greenwell, and Ritchey.

The University Learning Center, located on the first floor of Westside Hall, provides tutoring for basic studies mathematics and statistics courses.  Math Services also provides course-specific review and problem sessions, and help with math study skills and math anxiety.

No appointment is needed during open lab hours.

Web: [[www.uncw.edu/stuaff/uls|http://www.uncw.edu/stuaff/uls]]
Phone: 962-7857
Email: ULC@uncw.edu

/%
Please note that the following lecture outlines from Fall 2006 are under revision.  Topics covered in Fall 2007 may differ.

*[[Overview (pdf)|lectures/mat346lecture0.pdf]]
*[[Problem Studies (pdf)|lectures/mat346lecture2.pdf]]
*[[Egypt and Mesopotamia (pdf)|lectures/mat346lecture3.pdf]]
*[[Greek Mathematics to the Time of Euclid (pdf)|lectures/mat346lecture4.pdf]]
*[[Euclid and his Elements (pdf)|lectures/mat346lecture4b.pdf]]
*[[Greek Mathematics from Archimedes to Ptolemy (pdf)|lectures/mat346lecture6.pdf]]
*[[Greek Mathematics from Diophantus to Hypatia (pdf)|lectures/mat346lecture7.pdf]]
*[[Ancient and Medieval China (pdf)|lectures/mat346lecture8.pdf]]
*[[Ancient and Medieval India (pdf)|lectures/mat346lecture9b.pdf]]
*[[Mathematics in Medieval Europe (pdf)|lectures/mat346lecture10.pdf]]
*[[Mathematics in the Renaissance 1 (pdf)|lectures/mat346lecture11.pdf]]
*[[Mathematics in the Renaissance 2 (pdf)|lectures/mat346lecture12.pdf]]
*[[Calculus in the Seventeenth Century (pdf)|lectures/mat346lecture14.pdf]]
*[[Algebra and Number Theory in the Eighteenth Century (pdf)|lectures/mat346lecture16.pdf]]
*[[Geometry in the Eighteenth Century (pdf)|lectures/mat346lecture17.pdf]]
*[[Algebra and Number Theory in the Nineteenth Century 1 (pdf)|lectures/mat346lecture18.pdf]]
*[[Algebra and Number Theory in the Nineteenth Century 2 (pdf)|lectures/mat346lecture19.pdf]]
*[[Analysis in the Nineteenth Century 1 (pdf)|lectures/mat346lecture21.pdf]]
*[[Analysis in the Nineteenth Century 2 (pdf)|lectures/mat346lecture22.pdf]]
%/

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question: 
What happens to the oxygen concentration in a pond over the long run?
</part>

<part data hidden>
A small pond may normally contain 12 units of dissolved oxygen in a fixed volume of water.  Suppose that the oxygen concentration in the pond $t$ weeks after introduction of a quantity of organic waste is given by
$$f(t) = \frac{12t^2 - 15t + 12}{t^2 + 1}.$$
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
Outline "Outline" ./outline
>>

<<tiddler [[LGR]]>>

<part outline hidden>
* $f(x)$ notation
*Linear Function
*Supply, Demand, and Equilibrium Quantity
*Marginal Cost
*Revenue, Profit, and ~Break-Even Quantity
</part>
<part LQ hidden>
Leading Question:  
How many units must be sold for a firm to break even?
</part>
<part data hidden>
A firm finds that the total cost $C(x)$ in dollars of producing and selling $x$ units is given by $C(x) = 20x + 100.$  Management plans to charge 24 dollars per unit.
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>

<part LQ hidden>
Leading Question:  
With an inflation rate averaging 5 percent per year, how long will it take for prices to double?
</part>

<part data hidden>
Our answer may depend on the chosen compounding period or accepted approximation rules (such as the rule of 72).
</part>

[[Schedule]]
[[Notable Dates]]
[[Assignments]]
[[Course Policies]]
[[Contact Information]]
[[Learning Center]]
<<toggleSideBar '' '' hide>>

/***
|''Name:''|MathSVGPlugin|
|''Description:''|This plugin translates a subset of the LaTeX math notation to MathML with a customisable  image fallback when MathML is not supported. It also provides an easy way to produce mathematical SVG graphics with dynamical features and animation.|
|''Version:''|1.1|
|''Date:''|2009-05-05|
|''Source:''|http://www.math.ist.utl.pt/~psoares/mathsvg.html|
|''Author:''|Paulo Soares|
|''License:''|[[GNU Lesser General Public License|http://www.gnu.org/licences/lgpl.html]]|
|''~CoreVersion:''|2.5.0|
!Original copyright notice
{{{
ASCIIMathML.js
==============
Version 2.1 Oct 8, 2008, (c) Peter Jipsen http://www.chapman.edu/~jipsen
This version extends ASCIIMathML.js with LaTeXMathML.js and ASCIIsvg.js.
Latest version at http://www.chapman.edu/~jipsen/mathml/ASCIIMathML.js
If you use it on a webpage, please send the URL to jipsen@chapman.edu

The LaTeXMathML modifications were made by Douglas Woodall, June 2006.
(for details see header on the LaTeXMathML part in middle of file)
Extensive clean-up and improvements by Paulo Soares, Oct 2007.

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT 
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS 
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License 
(at http://www.gnu.org/licences/lgpl.html) for more details.
}}}
!~MathSVG code (minified)
***/
//{{{
Math.sec=function(a){return 1/Math.cos(a)};Math.csc=function(a){return 1/Math.sin(a)};Math.cot=function(a){return 1/Math.tan(a)};Math.asec=function(a){return Math.acos(1/a)};Math.acsc=function(a){return Math.asin(1/a)};Math.acot=function(a){return Math.atan(1/a)};Math.sinh=function(a){return(Math.exp(a)-Math.exp(-a))/2};Math.cosh=function(a){return(Math.exp(a)+Math.exp(-a))/2};Math.tanh=function(a){return(Math.exp(a)-Math.exp(-a))/(Math.exp(a)+Math.exp(-a))};Math.sech=function(a){return 1/Math.cosh(a)};Math.csch=function(a){return 1/Math.sinh(a)};Math.coth=function(a){return 1/Math.tanh(a)};Math.asinh=function(a){return Math.log(a+Math.sqrt(a*a+1))};Math.acosh=function(a){return Math.log(a+Math.sqrt(a*a-1))};Math.atanh=function(a){return Math.log((1+a)/(1-a))/2};Math.sech=function(a){return 1/Math.cosh(a)};Math.csch=function(a){return 1/Math.sinh(a)};Math.coth=function(a){return 1/Math.tanh(a)};Math.asech=function(a){return Math.acosh(1/a)};Math.acsch=function(a){return 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ddy=Math.max(0,Math.floor(-Math.log(dy+1e-9)/Math.log(10))+1);options.marker="-|"+(options.marker||"-");options.strokewidth=(options.strokewidth||SVG.attr.axesstrokewidth)/SVG.factor;options.stroke=options.stroke||SVG.attr.axesstroke;var temp=options.stroke;options.markerstroke=options.stroke;options.markersize=fontsize*SVG.factor;var list1=[],label1=[];start=orig[0]+dx;stop=SVG.xmax-0.25*dx;for(x=start;x<stop;x+=dx){list1.push([x,orig[1]]);label1.push(String(x.toFixed(ddx)))}list1.push([SVG.xmax-border/SVG.xunitlength,orig[1]]);label1.push("");var list2=[],label2=[];start=orig[0]-dx;stop=SVG.xmin+0.25*dx;for(x=start;x>stop;x-=dx){list2.push([x,orig[1]]);label2.push(String(x.toFixed(ddx)))}list2.push([SVG.xmin+border/SVG.xunitlength,orig[1]]);label2.push("");list2.reverse();list2=list2.concat(list1);if(options.ticklabels!=false){label2.reverse();options.label=label2.concat(label1);options.pos=(SVG.height-origin[1]>2*fontsize)?"S":"N"}var group=getSVGElement("Axes","g");$(group.node).empty();var tempNode=SVG.canvas;SVG.canvas=group.node;path(list2,options);list1=[],label1=[];start=orig[1]+dy;stop=SVG.ymax-0.25*dy;for(y=start;y<stop;y+=dy){list1.push([orig[0],y]);label1.push(String(y.toFixed(ddy)))}list1.push([orig[0],SVG.ymax-border/SVG.yunitlength]);label1.push("");list2=[];label2=[];start=orig[1]-dy;stop=SVG.ymin+0.25*dy;for(y=start;y>stop;y-=dy){list2.push([orig[0],y]);label2.push(String(y.toFixed(ddy)))}list2.push([orig[0],SVG.ymin+border/SVG.yunitlength]);label2.push("");list2.reverse();list2=list2.concat(list1);if(options.ticklabels!=false){label2.reverse();options.label=label2.concat(label1);options.pos=(origin[0]>2*fontsize)?"W":"E"}options.stroke=temp;path(list2,options);SVG.canvas=tempNode;appendSVG(group)}function list(fun,tmin,tmax,points){var inc=(tmax-tmin)/points;if(inc<=0||fun.length==0){return}var t,pth,g=[],xt,yt;for(t=1;t>=0;t--){if($.isFunction(fun[t])){g[t]=fun[t]}else{if(typeof fun[t]=="string"){with(Math){eval("g["+t+"] = function(x){return "+fun[t]+"}")}}else{return}}}if(g.length<2){return}pth=[];for(t=tmin;t<=tmax;t+=inc){xt=g[0](t);yt=g[1](t);if(isFinite(xt)&&isFinite(yt)){pth[pth.length]=[xt,yt]}}return pth}function plot(fun,options){options=options||{};var i,steps=options.steps||[];var leftMarkers=options.leftMarkers||"-";var rightMarkers=options.rightMarkers||"-";if(steps.length===0){plotter(fun,options)}else{var n_steps=steps.length-1;options.max=steps[0];options.marker="--"+leftMarkers.charAt(0);plotter(fun,options);for(i=0;i<n_steps;i++){options.max=steps[i+1];options.min=steps[i];options.marker=rightMarkers.charAt((rightMarkers.length>i)?i:0)+"-"+leftMarkers.charAt((leftMarkers.length>i+1)?i+1:0);plotter(fun,options)}options.max=null;options.min=steps[n_steps];options.marker=rightMarkers.charAt((rightMarkers.length==n_steps)?n_steps-1:0)+"--";plotter(fun,options)}}function plotter(fun,options){options=options||{};options.closed=false;options.curve="";var xmin=(options.min==null)?SVG.xmin:options.min;var xmax=(options.max==null)?SVG.xmax:options.max;var points=getOption("points",options);var pth=list(["x",fun],xmin,xmax,points);if(pth){path(pth,options)}}function area(fun1,fun2,options){options=options||{};options.curve="";options.closed=true;var xmin=(options.min==null)?SVG.xmin:options.min;var xmax=(options.max==null)?SVG.xmax:options.max;var points=getOption("points",options);var pth1=list(["x",fun1],xmin,xmax,points);var pth2=list(["x",fun2],xmin,xmax,points);if(pth1&&pth2){pth2.reverse();pth1=pth1.concat(pth2);path(pth1,options)}}function polarPlot(fun,options){var g1,g2;if(typeof fun=="string"){with(Math){eval("g1 = function(x){return ("+fun+")*cos(x)}");eval("g2 = function(x){return ("+fun+")*sin(x)}")}}else{if($.isFunction(fun)){with(Math){eval("g1 = function(x){return fun(x)*cos(x)}");eval("g2 = function(x){return fun(x)*sin(x)}")}}}parametricPlot(g1,g2,options)}function parametricPlot(fun1,fun2,options){options=options||{};options.closed=false;options.curve="";var xmin=(options.min==null)?0:options.min;var xmax=(options.max==null)?2*Math.PI:options.max;var points=getOption("points",options);var pth=list([fun1,fun2],xmin,xmax,points);if(pth){path(pth,options)}}function slopeField(fun,options){options=options||{};var g=fun;if(typeof fun=="string"){with(Math){eval("g = function(x,y){return "+fun+"}")}}var gxy,x,y,u,v,dz;var dx=(options.dx==null)?1:options.dx;var dy=(options.dy==null)?1:options.dy;dz=Math.sqrt(dx*dx+dy*dy)/6;var xmin=Math.ceil(SVG.xmin/dx);var ymin=Math.ceil(SVG.ymin/dy);for(x=xmin;x<=SVG.xmax;x+=dx){for(y=ymin;y<=SVG.ymax;y+=dy){gxy=g(x,y);if(!isNaN(gxy)){if(Math.abs(gxy)=="Infinity"){u=0;v=dz}else{u=dz/Math.sqrt(1+gxy*gxy);v=gxy*u}line([x-u,y-v],[x+u,y+v],options)}}}}return{dynamic:{},removePictures:function(obj){var pictures=obj?[obj]:$(".svgGraph");$(pictures).each(function(){var target=this.parentNode;$(this).remove();$(target).css({color:"red",background:"yellow"});$(target).text("Missing picture: your  browser does not support inline SVG");window.setTimeout(function(){$(target).remove()},10000)})},drawPictures:function(obj){var options,xmin,xmax,ymin,ymax;var pictures=obj?[obj]:$(".svgGraph");$(pictures).each(function(){SVG=new pictureObject();options=this.getAttribute("options");if(options!=""){with(Math){eval("options="+options)}setOptions(options)}else{options={}}SVG.width=options.width||SVG.width;SVG.height=options.height||SVG.height;SVG.coords=options.coords||SVG.coords;SVG.borderwidth=options.borderwidth||SVG.borderwidth;SVG.borderstroke=options.borderstroke||SVG.borderstroke;if(options.pan==false){SVG.pan=false}SVG.src=this.getAttribute("script");var container=this.parentNode;container.removeChild(this);options.scales=options.scales||[];switch(options.scales.length){case 0:xmin=SVG.xmin;xmax=SVG.xmax;ymin=null;ymax=null;break;case 2:xmin=options.scales[0];xmax=options.scales[1];ymin=null;ymax=null;break;case 4:xmin=options.scales[0];xmax=options.scales[1];ymin=options.scales[2];ymax=options.scales[3];break;default:return}if(xmin>=xmax){throw"Incorrect values: xmax<=xmin."}var xunitlength=SVG.width/(xmax-xmin);if(typeof ymin!="number"){ymin=-SVG.height/(2*xunitlength);ymax=-ymin}if(ymin>=ymax){throw"Incorrect values: ymax<=ymin."}SVG.xmin=xmin;SVG.xmax=xmax;SVG.ymin=ymin;SVG.ymax=ymax;setScales();SVG.id=Math.randomString(chars,20);var qnode=createSVGElement("svg");qnode.id=SVG.id;qnode.setAttribute("xmlns","http://www.w3.org/2000/svg");var node=createSVGElement("clipPath");node.id=SVG.id+"ClipPath";var node2=createSVGElement("path");$(node).append(node2);node2=createSVGElement("defs");node2.id=SVG.id+"_Defs";$(node2).append(node);$(qnode).append(node2);node=createSVGElement("rect");node.setAttribute("class","svgBackground");node.setAttribute("x","0");node.setAttribute("y","0");node.setAttribute("width","100%");node.setAttribute("height","100%");node.setAttribute("stroke",SVG.borderstroke);node.setAttribute("stroke-width",SVG.borderwidth);node.setAttribute("fill",SVG.attr.backgroundcolor);node.setAttribute("fill-opacity",SVG.attr.backgroundopacity);$(qnode).append(node);node=createSVGElement("g");node.id=SVG.id+"Canvas";node.setAttribute("clip-path","url(#"+SVG.id+"ClipPath)");SVG.canvas=node;$(qnode).append(node);if(SVG.coords!="none"){node=createSVGElement("text");node.id=SVG.id+"Coords";node.setAttribute("class","svgCoords");node.setAttribute("text-anchor","end");node.setAttribute("font-size",(SVG.attr.fontsize*0.8));$(qnode).append(node)}$(container).append(qnode);container.style.position="relative";node=MSVG.createElementXHTML("span",SVG.id+"mml");$(container).append(node);node=MSVG.createElementXHTML("span",SVG.id+"toolbar");node.style.position="absolute";node.style.textAlign="left";node.style.zIndex=10;node2=setButton("Update","Edit script",function(){updateButton(this)});$(node).append(node2);node2=setButton("SVG","View SVG code",function(){exportSVG(this)});$(node).append(node2);node2=setButton("-","Zoom out",function(){changeScales(1.25)});$(node).append(node2);node2=setButton("+","Zoom in",function(){changeScales(0.8)});$(node).append(node2);node2=setButton("\u2191","Enlarge picture",function(){changeSize(0.8)});$(node).append(node2);node2=setButton("\u2193","Reduce picture",function(){changeSize(1.25)});$(node).append(node2);$(node).append("<br />");node2=MSVG.createElementXHTML("textarea",SVG.id+"src");$(node2).attr({rows:8,cols:80});$(node).append(node2);$(node).hide();$(container).append(node);setAction("mousemove",updateCoord);setAction("mouseout",removeCoord);setAction("mouseover",switchTo);setAction("mousedown",onClick);if(SVG.pan){setAction("mouseup",onDrop)}if(window.addEventListener){var evt=$.browser.mozilla?"DOMMouseScroll":"mousewheel";qnode.addEventListener(evt,onWheel,false)}setSize();translateAndEval(SVG.id)})}}}(jQuery);
//}}}
/***
!~TiddlyWiki formatters
***/
//{{{
if(!version.extensions.MathSVGPlugin) { //# ensure that the plugin is only installed once
version.extensions.MathSVGPlugin = {installed: true};
MSVG.generic();

config.formatterHelpers.MathSVGHelper = function(w) {
  this.lookaheadRegExp.lastIndex = w.matchStart;
  var lookaheadMatch = this.lookaheadRegExp.exec(w.source);
  if(lookaheadMatch){
    var eq = MSVG.parseMath(lookaheadMatch[1],this.displaystyle);
    if(this.displaystyle){
      var node = createTiddlyElement(w.output,"div");
      node.style.textAlign='center';
      node.appendChild(eq);
      w.output.appendChild(node);
    } else {w.output.appendChild(eq);}
    w.nextMatch = lookaheadMatch.index + lookaheadMatch[0].length;
  }
}

config.formatters.push( {
  name: "clatex",
  match: "\\$\\$",
  lookaheadRegExp: /\$\$((?:.|\n)*?)\$\$/mg,
  displaystyle: true,
  handler: config.formatterHelpers.MathSVGHelper
})

config.formatters.push( {
  name: "clatex2",
  match: "\\\\\\\[",
  lookaheadRegExp: /\\\[\s*(.*?)\s*\\\]/mg,
  displaystyle: true,
  handler: config.formatterHelpers.MathSVGHelper
})

config.formatters.push( {
  name: "latex",
  match: "\\$",
  lookaheadRegExp: /\$((?:.|\n)*?)\$/mg,
  displaystyle: false,
  handler: config.formatterHelpers.MathSVGHelper
})

config.formatters.push( {
  name: "graph",
  match: "\\(:graph",
  lookaheadRegExp: /\(:graph(\((.*?),?\s?(\{.+\})?\))?[\s]+((?:.|\n)*?)[\s]+:\)/mg,
  handler: function(w){
  this.lookaheadRegExp.lastIndex = w.matchStart;
  var lookaheadMatch = this.lookaheadRegExp.exec(w.source);
  if(lookaheadMatch){
    var element = (lookaheadMatch[2] == "inline") ? "span" : "div";
    var eq = createTiddlyElement(w.output,element);
    switch(lookaheadMatch[2]){
    case "center":
      eq.style.marginLeft = "auto";
      eq.style.marginRight = "auto";
      break;
    case "left":
      eq.style.cssFloat = "left";
      break;
    case "right":
      eq.style.cssFloat = "right";
    }
    var svg = createTiddlyElement(eq,"embed");
    svg.className="svgGraph";
    svg.setAttribute('options',lookaheadMatch[3]||"");
    svg.setAttribute('script',lookaheadMatch[4]);
    ASVG.drawPictures(svg);
    w.nextMatch = lookaheadMatch.index + lookaheadMatch[0].length;
  }
  }
})
}
//}}}

/***
The script should not be edited. All available options can be set by the following variables:
***/
//{{{
//MSVG.showFormulaOnMouseOver = false; //show LaTeX code on mouse over the equation
//MSVG.latexImages = false; //set to true to force the use of an external converter
//MSVG.latexConverter = "http://www.yourequations.com/eq.latex?"; //link to external converter
//MSVG.mathColor = "green"; //font color
//MSVG.mathFontSize = ""; //font size
//MSVG.mathFontFamily = ""; //font family
//}}}
/***
New symbols or commands can be defined here:
***/
//{{{
 var commands = ["nle","R","diagup","varnothing","ind","DD"];
 var symbols = ["\u2270","\u211D","\u2571","\u2205","\u2AEB","\\frac{d}{dr}"];
 MSVG.define(commands,symbols);
//}}}

(:graph({width:300}) axes(); plot("sin(x)"); :)

(:graph({width:300,height:200,scales:[-3,3,-2,2]})
axes();
grid({dx:0.5,dy:0.5});
plot("(x-2)*(x-1)*x*(x+1)*(x+2)/2",{min:-2.5,max:2.5});
:)

$\diagup X\ind Y \tilde{A} \varnothing$

$$A = \left(\begin{array}{c c c}
1-x & 0 & 0 \\ 0 & 1-x & 0 \\ 0 & 0 & 1-x \end{array}\right)$$

$\sum a_i + \sum_{i=0}^{+\infty} b_i$

$f(x) = \left\{\begin{array}{l l}
x^2 \sin \frac1x & \textrm{if } x \ne 0, \\
0 & \textrm{if } x = 0 .
\end{array}\right.$

$\displaystyle{ \lim_{x\to\infty} f(x) = k \choose r + \frac ab \sum_{n=1}^{+\infty} a_n + \left\{ \frac{1}{13} \sum_{n=1}^{+\infty} b_n \right\} }$

*Test 1:  Thursday, September 24
*Test 2:  Thursday, November 5
*Final: Tuesday, December 8, 08:00-11:00a

Type the text for 'New Tiddler'

<!--{{{-->
<div class='header' macro='gradient vert [[ColorPalette::PrimaryLight]] [[ColorPalette::PrimaryMid]]'>
<div class='headerShadow'>
<span class='siteTitle' refresh='content' tiddler='SiteTitle'></span>&nbsp;
<span class='siteSubtitle' refresh='content' tiddler='SiteSubtitle'></span>
</div>
<div class='headerForeground'>
<span class='siteTitle' refresh='content' tiddler='SiteTitle'></span>&nbsp;
<span class='siteSubtitle' refresh='content' tiddler='SiteSubtitle'></span>
</div>
</div><!-- horizontal MainMenu -->
<div id='topMenu' refresh='content' tiddler='MainMenu'></div>
<!--original MainMenu menu
<div id='mainMenu' refresh='content' tiddler='MainMenu'></div>
-->
<div id='sidebar'>
<div id='sidebarOptions' refresh='content' tiddler='SideBarOptions'></div>
<div id='sidebarTabs' refresh='content' force='true' tiddler='SideBarTabs'></div>
</div>
<div id='displayArea'>
<div id='messageArea'></div>
<div id='tiddlerDisplay'></div>
</div>
<!--}}}-->

/***
|<html><a name="Top"/></html>''Name:''|PartTiddlerPlugin|
|''Version:''|1.0.9 (2007-07-14)|
|''Source:''|http://tiddlywiki.abego-software.de/#PartTiddlerPlugin|
|''Author:''|UdoBorkowski (ub [at] abego-software [dot] de)|
|''Licence:''|[[BSD open source license]]|
|''CoreVersion:''|2.1.3|
|''Browser:''|Firefox 1.0.4+; InternetExplorer 6.0|
!Table of Content<html><a name="TOC"/></html>
* <html><a href="javascript:;" onclick="window.scrollAnchorVisible('Description',null, event)">Description, Syntax</a></html>
* <html><a href="javascript:;" onclick="window.scrollAnchorVisible('Applications',null, event)">Applications</a></html>
** <html><a href="javascript:;" onclick="window.scrollAnchorVisible('LongTiddler',null, event)">Refering to Paragraphs of a Longer Tiddler</a></html>
** <html><a href="javascript:;" onclick="window.scrollAnchorVisible('Citation',null, event)">Citation Index</a></html>
** <html><a href="javascript:;" onclick="window.scrollAnchorVisible('TableCells',null, event)">Creating "multi-line" Table Cells</a></html>
** <html><a href="javascript:;" onclick="window.scrollAnchorVisible('Tabs',null, event)">Creating Tabs</a></html>
** <html><a href="javascript:;" onclick="window.scrollAnchorVisible('Sliders',null, event)">Using Sliders</a></html>
* <html><a href="javascript:;" onclick="window.scrollAnchorVisible('Revisions',null, event)">Revision History</a></html>
* <html><a href="javascript:;" onclick="window.scrollAnchorVisible('Code',null, event)">Code</a></html>
!Description<html><a name="Description"/></html>
With the {{{<part aPartName> ... </part>}}} feature you can structure your tiddler text into separate (named) parts. 
Each part can be referenced as a "normal" tiddler, using the "//tiddlerName//''/''//partName//" syntax (e.g. "About/Features").  E.g. you may create links to the parts (e.g. {{{[[Quotes/BAX95]]}}} or {{{[[Hobbies|AboutMe/Hobbies]]}}}), use it in {{{<<tiddler...>>}}} or {{{<<tabs...>>}}} macros etc.


''Syntax:'' 
|>|''<part'' //partName// [''hidden''] ''>'' //any tiddler content// ''</part>''|
|//partName//|The name of the part. You may reference a part tiddler with the combined tiddler name "//nameOfContainerTidder//''/''//partName//. <<br>>If you use a partName containing spaces you need to quote it (e.g. {{{"Major Overview"}}} or {{{[[Shortcut List]]}}}).|
|''hidden''|When defined the content of the part is not displayed in the container tiddler. But when the part is explicitly referenced (e.g. in a {{{<<tiddler...>>}}} macro or in a link) the part's content is displayed.|
|<html><i>any&nbsp;tiddler&nbsp;content</i></html>|<html>The content of the part.<br>A part can have any content that a "normal" tiddler may have, e.g. you may use all the formattings and macros defined.</html>|
|>|~~Syntax formatting: Keywords in ''bold'', optional parts in [...]. 'or' means that exactly one of the two alternatives must exist.~~|
<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!Applications<html><a name="Applications"/></html>
!!Refering to Paragraphs of a Longer Tiddler<html><a name="LongTiddler"/></html>
Assume you have written a long description in a tiddler and now you want to refer to the content of a certain paragraph in that tiddler (e.g. some definition.) Just wrap the text with a ''part'' block, give it a nice name, create a "pretty link" (like {{{[[Discussion Groups|Introduction/DiscussionGroups]]}}}) and you are done.

Notice this complements the approach to first writing a lot of small tiddlers and combine these tiddlers to one larger tiddler in a second step (e.g. using the {{{<<tiddler...>>}}} macro). Using the ''part'' feature you can first write a "classic" (longer) text that can be read "from top to bottom" and later "reuse" parts of this text for some more "non-linear" reading.

<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!!Citation Index<html><a name="Citation"/></html>
Create a tiddler "Citations" that contains your "citations". 
Wrap every citation with a part and a proper name. 

''Example''
{{{
<part BAX98>Baxter, Ira D. et al: //Clone Detection Using Abstract Syntax Trees.// 
in //Proc. ICSM//, 1998.</part>

<part BEL02>Bellon, Stefan: //Vergleich von Techniken zur Erkennung duplizierten Quellcodes.// 
Thesis, Uni Stuttgart, 2002.</part>

<part DUC99>Ducasse, Stéfane et al: //A Language Independent Approach for Detecting Duplicated Code.// 
in //Proc. ICSM//, 1999.</part>
}}}

You may now "cite" them just by using a pretty link like {{{[[Citations/BAX98]]}}} or even more pretty, like this {{{[[BAX98|Citations/BAX98]]}}}.

<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!!Creating "multi-line" Table Cells<html><a name="TableCells"/></html>
You may have noticed that it is hard to create table cells with "multi-line" content. E.g. if you want to create a bullet list inside a table cell you cannot just write the bullet list
{{{
* Item 1
* Item 2
* Item 3
}}}
into a table cell (i.e. between the | ... | bars) because every bullet item must start in a new line but all cells of a table row must be in one line.

Using the ''part'' feature this problem can be solved. Just create a hidden part that contains the cells content and use a {{{<<tiddler >>}}} macro to include its content in the table's cell.

''Example''
{{{
|!Subject|!Items|
|subject1|<<tiddler ./Cell1>>|
|subject2|<<tiddler ./Cell2>>|

<part Cell1 hidden>
* Item 1
* Item 2
* Item 3
</part>
...
}}}

Notice that inside the {{{<<tiddler ...>>}}} macro you may refer to the "current tiddler" using the ".".

BTW: The same approach can be used to create bullet lists with items that contain more than one line.

<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!!Creating Tabs<html><a name="Tabs"/></html>
The build-in {{{<<tabs ...>>}}} macro requires that you defined an additional tiddler for every tab it displays. When you want to have "nested" tabs you need to define a tiddler for the "main tab" and one for every tab it contains. I.e. the definition of a set of tabs that is visually displayed at one place is distributed across multiple tiddlers.

With the ''part'' feature you can put the complete definition in one tiddler, making it easier to keep an overview and maintain the tab sets.

''Example''
The standard tabs at the sidebar are defined by the following eight tiddlers:
* SideBarTabs
* TabAll
* TabMore
* TabMoreMissing
* TabMoreOrphans
* TabMoreShadowed
* TabTags
* TabTimeline

Instead of these eight tiddlers one could define the following SideBarTabs tiddler that uses the ''part'' feature:
{{{
<<tabs txtMainTab 
    Timeline Timeline SideBarTabs/Timeline 
    All 'All tiddlers' SideBarTabs/All 
    Tags 'All tags' SideBarTabs/Tags 
    More 'More lists' SideBarTabs/More>>
<part Timeline hidden><<timeline>></part>
<part All hidden><<list all>></part>
<part Tags hidden><<allTags>></part>
<part More hidden><<tabs txtMoreTab 
    Missing 'Missing tiddlers' SideBarTabs/Missing 
    Orphans 'Orphaned tiddlers' SideBarTabs/Orphans 
    Shadowed 'Shadowed tiddlers' SideBarTabs/Shadowed>></part>
<part Missing hidden><<list missing>></part>
<part Orphans hidden><<list orphans>></part>
<part Shadowed hidden><<list shadowed>></part>
}}}

Notice that you can easily "overwrite" individual parts in separate tiddlers that have the full name of the part.

E.g. if you don't like the classic timeline tab but only want to see the 100 most recent tiddlers you could create a tiddler "~SideBarTabs/Timeline" with the following content:
{{{
<<forEachTiddler 
		sortBy 'tiddler.modified' descending 
		write '(index < 100) ? "* [["+tiddler.title+"]]\n":""'>>
}}}
<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!!Using Sliders<html><a name="Sliders"/></html>
Very similar to the build-in {{{<<tabs ...>>}}} macro (see above) the {{{<<slider ...>>}}} macro requires that you defined an additional tiddler that holds the content "to be slid". You can avoid creating this extra tiddler by using the ''part'' feature

''Example''
In a tiddler "About" we may use the slider to show some details that are documented in the tiddler's "Details" part.
{{{
...
<<slider chkAboutDetails About/Details details "Click here to see more details">>
<part Details hidden>
To give you a better overview ...
</part>
...
}}}

Notice that putting the content of the slider into the slider's tiddler also has an extra benefit: When you decide you need to edit the content of the slider you can just doubleclick the content, the tiddler opens for editing and you can directly start editing the content (in the part section). In the "old" approach you would doubleclick the tiddler, see that the slider is using tiddler X, have to look for the tiddler X and can finally open it for editing. So using the ''part'' approach results in a much short workflow.

<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!Revision history<html><a name="Revisions"/></html>
* v1.0.9 (2007-07-14)
** Bugfix: Error when using the SideBarTabs example and switching between "More" and "Shadow". Thanks to cmari for reporting the issue.
* v1.0.8 (2007-06-16)
** Speeding up display of tiddlers containing multiple pard definitions. Thanks to Paco Rivière for reporting the issue.
** Support "./partName" syntax inside <<tabs ...>> macro
* v1.0.7 (2007-03-07)
** Bugfix: <<tiddler "./partName">> does not always render correctly after a refresh (e.g. like it happens when using the "Include" plugin). Thanks to Morris Gray for reporting the bug.
* v1.0.6 (2006-11-07)
** Bugfix: cannot edit tiddler when UploadPlugin by Bidix is installed. Thanks to José Luis González Castro for reporting the bug.
* v1.0.5 (2006-03-02)
** Bugfix: Example with multi-line table cells does not work in IE6. Thanks to Paulo Soares for reporting the bug.
* v1.0.4 (2006-02-28)
** Bugfix: Shadow tiddlers cannot be edited (in TW 2.0.6). Thanks to Torsten Vanek for reporting the bug.
* v1.0.3 (2006-02-26)
** Adapt code to newly introduced Tiddler.prototype.isReadOnly() function (in TW 2.0.6). Thanks to Paulo Soares for reporting the problem.
* v1.0.2 (2006-02-05)
** Also allow other macros than the "tiddler" macro use the "." in the part reference (to refer to "this" tiddler)
* v1.0.1 (2006-01-27)
** Added Table of Content for plugin documentation. Thanks to RichCarrillo for suggesting.
** Bugfix: newReminder plugin does not work when PartTiddler is installed. Thanks to PauloSoares for reporting.
* v1.0.0 (2006-01-25)
** initial version
<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!Code<html><a name="Code"/></html>
<html><sub><a href="javascript:;" onclick="window.scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>
***/
//{{{
//============================================================================
//                           PartTiddlerPlugin

// Ensure that the PartTiddler Plugin is only installed once.
//
if (!version.extensions.PartTiddlerPlugin) {



version.extensions.PartTiddlerPlugin = {
    major: 1, minor: 0, revision: 9,
    date: new Date(2007, 6, 14), 
    type: 'plugin',
    source: "http://tiddlywiki.abego-software.de/#PartTiddlerPlugin"
};

if (!window.abego) window.abego = {};
if (version.major < 2) alertAndThrow("PartTiddlerPlugin requires TiddlyWiki 2.0 or newer.");

//============================================================================
// Common Helpers

// Looks for the next newline, starting at the index-th char of text. 
//
// If there are only whitespaces between index and the newline 
// the index behind the newline is returned, 
// otherwise (or when no newline is found) index is returned.
//
var skipEmptyEndOfLine = function(text, index) {
	var re = /(\n|[^\s])/g;
	re.lastIndex = index;
	var result = re.exec(text);
	return (result && text.charAt(result.index) == '\n') 
			? result.index+1
			: index;
}


//============================================================================
// Constants

var partEndOrStartTagRE = /(<\/part>)|(<part(?:\s+)((?:[^>])+)>)/mg;
var partEndTagREString = "<\\/part>";
var partEndTagString = "</part>";

//============================================================================
// Plugin Specific Helpers

// Parse the parameters inside a <part ...> tag and return the result.
//
// @return [may be null] {partName: ..., isHidden: ...}
//
var parseStartTagParams = function(paramText) {
	var params = paramText.readMacroParams();
	if (params.length == 0 || params[0].length == 0) return null;
	
	var name = params[0];
	var paramsIndex = 1;
	var hidden = false;
	if (paramsIndex < params.length) {
		hidden = params[paramsIndex] == "hidden";
		paramsIndex++;
	}
	
	return {
		partName: name, 
		isHidden: hidden
	};
}

// Returns the match to the next (end or start) part tag in the text, 
// starting the search at startIndex.
// 
// When no such tag is found null is returned, otherwise a "Match" is returned:
// [0]: full match
// [1]: matched "end" tag (or null when no end tag match)
// [2]: matched "start" tag (or null when no start tag match)
// [3]: content of start tag (or null if no start tag match)
//
var findNextPartEndOrStartTagMatch = function(text, startIndex) {
	var re = new RegExp(partEndOrStartTagRE);
	re.lastIndex = startIndex;
	var match = re.exec(text);
	return match;
}

//============================================================================
// Formatter

// Process the <part ...> ... </part> starting at (w.source, w.matchStart) for formatting.
//
// @return true if a complete part section (including the end tag) could be processed, false otherwise.
//
var handlePartSection = function(w) {
	var tagMatch = findNextPartEndOrStartTagMatch(w.source, w.matchStart);
	if (!tagMatch) return false;
	if (tagMatch.index != w.matchStart || !tagMatch[2]) return false;

	// Parse the start tag parameters
	var arguments = parseStartTagParams(tagMatch[3]);
	if (!arguments) return false;
	
	// Continue processing
	var startTagEndIndex = skipEmptyEndOfLine(w.source, tagMatch.index + tagMatch[0].length);
	var endMatch = findNextPartEndOrStartTagMatch(w.source, startTagEndIndex);
	if (endMatch && endMatch[1]) {
		if (!arguments.isHidden) {
			w.nextMatch = startTagEndIndex;
			w.subWikify(w.output,partEndTagREString);
		}
		w.nextMatch = skipEmptyEndOfLine(w.source, endMatch.index + endMatch[0].length);
		
		return true;
	}
	return false;
}

config.formatters.push( {
    name: "part",
    match: "<part\\s+[^>]+>",
	
	handler: function(w) {
		if (!handlePartSection(w)) {
			w.outputText(w.output,w.matchStart,w.matchStart+w.matchLength);
		}
	}
} )

//============================================================================
// Extend "fetchTiddler" functionality to also recognize "part"s of tiddlers 
// as tiddlers.

var currentParent = null; // used for the "." parent (e.g. in the "tiddler" macro)

// Return the match to the first <part ...> tag of the text that has the
// requrest partName.
//
// @return [may be null]
//
var findPartStartTagByName = function(text, partName) {
	var i = 0;
	
	while (true) {
		var tagMatch = findNextPartEndOrStartTagMatch(text, i);
		if (!tagMatch) return null;

		if (tagMatch[2]) {
			// Is start tag
	
			// Check the name
			var arguments = parseStartTagParams(tagMatch[3]);
			if (arguments && arguments.partName == partName) {
				return tagMatch;
			}
		}
		i = tagMatch.index+tagMatch[0].length;
	}
}

// Return the part "partName" of the given parentTiddler as a "readOnly" Tiddler 
// object, using fullName as the Tiddler's title. 
//
// All remaining properties of the new Tiddler (tags etc.) are inherited from 
// the parentTiddler.
// 
// @return [may be null]
//
var getPart = function(parentTiddler, partName, fullName) {
	var text = parentTiddler.text;
	var startTag = findPartStartTagByName(text, partName);
	if (!startTag) return null;
	
	var endIndexOfStartTag = skipEmptyEndOfLine(text, startTag.index+startTag[0].length);
	var indexOfEndTag = text.indexOf(partEndTagString, endIndexOfStartTag);

	if (indexOfEndTag >= 0) {
		var partTiddlerText = text.substring(endIndexOfStartTag,indexOfEndTag);
		var partTiddler = new Tiddler();
		partTiddler.set(
						fullName,
						partTiddlerText,
						parentTiddler.modifier,
						parentTiddler.modified,
						parentTiddler.tags,
						parentTiddler.created);
		partTiddler.abegoIsPartTiddler = true;
		return partTiddler;
	}
	
	return null;
}

// Hijack the store.fetchTiddler to recognize the "part" addresses.
//
var hijackFetchTiddler = function() {
	var oldFetchTiddler = store.fetchTiddler ;
	store.fetchTiddler = function(title) {
		var result = oldFetchTiddler.apply(this, arguments);
		if (!result && title) {
			var i = title.lastIndexOf('/');
			if (i > 0) {
				var parentName = title.substring(0, i);
				var partName = title.substring(i+1);
				var parent = (parentName == ".") 
						? store.resolveTiddler(currentParent)
						: oldFetchTiddler.apply(this, [parentName]);
				if (parent) {
					return getPart(parent, partName, parent.title+"/"+partName);
				}
			}
		}
		return result;	
	};
};

// for debugging the plugin is not loaded through the systemConfig mechanism but via a script tag. 
// At that point in the "store" is not yet defined. In that case hijackFetchTiddler through the restart function.
// Otherwise hijack now.
if (!store) {
	var oldRestartFunc = restart;
	window.restart = function() {
		hijackFetchTiddler();
		oldRestartFunc.apply(this,arguments);
	};
} else
	hijackFetchTiddler();




// The user must not edit a readOnly/partTiddler
//

config.commands.editTiddler.oldIsReadOnlyFunction = Tiddler.prototype.isReadOnly;

Tiddler.prototype.isReadOnly = function() {
	// Tiddler.isReadOnly was introduced with TW 2.0.6.
	// For older version we explicitly check the global readOnly flag
	if (config.commands.editTiddler.oldIsReadOnlyFunction) {
		if (config.commands.editTiddler.oldIsReadOnlyFunction.apply(this, arguments)) return true;
	} else {
		if (readOnly) return true;
	}

	return this.abegoIsPartTiddler;
}

config.commands.editTiddler.handler = function(event,src,title)
{
	var t = store.getTiddler(title);
	// Edit the tiddler if it either is not a tiddler (but a shadowTiddler)
	// or the tiddler is not readOnly
	if(!t || !t.abegoIsPartTiddler)
		{
		clearMessage();
		story.displayTiddler(null,title,DEFAULT_EDIT_TEMPLATE);
		story.focusTiddler(title,"text");
		return false;
		}
}

// To allow the "./partName" syntax in macros we need to hijack 
// the invokeMacro to define the "currentParent" while it is running.
// 
var oldInvokeMacro = window.invokeMacro;
function myInvokeMacro(place,macro,params,wikifier,tiddler) {
	var oldCurrentParent = currentParent;
	if (tiddler) currentParent = tiddler;
	try {
		oldInvokeMacro.apply(this, arguments);
	} finally {
		currentParent = oldCurrentParent;
	}
}
window.invokeMacro = myInvokeMacro;

// To correctly support the "./partName" syntax while refreshing we need to hijack 
// the config.refreshers.tiddlers to define the "currentParent" while it is running.
// 
(function() {
	var oldTiddlerRefresher= config.refreshers.tiddler;
	config.refreshers.tiddler = function(e,changeList) {
		var oldCurrentParent = currentParent;
		try {
			currentParent = e.getAttribute("tiddler");
			return oldTiddlerRefresher.apply(this,arguments);
		} finally {
			currentParent = oldCurrentParent;
		}
	};
})();

// Support "./partName" syntax inside <<tabs ...>> macro
(function() {
	var extendRelativeNames = function(e, title) {
		var nodes = e.getElementsByTagName("a");
		for(var i=0; i<nodes.length; i++) {
			var node = nodes[i];
			var s = node.getAttribute("content");
			if (s && s.indexOf("./") == 0)
				node.setAttribute("content",title+s.substr(1));
		}
	};
	var oldHandler = config.macros.tabs.handler;
	config.macros.tabs.handler = function(place,macroName,params,wikifier,paramString,tiddler) {
		var result = oldHandler.apply(this,arguments);
		if (tiddler)
			extendRelativeNames(place, tiddler.title);
		return result;
	};
})();

// Scroll the anchor anchorName in the viewer of the given tiddler visible.
// When no tiddler is defined use the tiddler of the target given event is used.
window.scrollAnchorVisible = function(anchorName, tiddler, evt) {
	var tiddlerElem = null;
	if (tiddler) {
		tiddlerElem = document.getElementById(story.idPrefix + tiddler);
	}
	if (!tiddlerElem && evt) {
		var target = resolveTarget(evt);
		tiddlerElem = story.findContainingTiddler(target);
	}
	if (!tiddlerElem) return;

	var children = tiddlerElem.getElementsByTagName("a");
	for (var i = 0; i < children.length; i++) {
		var child = children[i];
		var name = child.getAttribute("name");
		if (name == anchorName) {
			var y = findPosY(child);
			window.scrollTo(0,y);
			return;
		}
	}
}

} // of "install only once"
//}}}

/***
<html><sub><a href="javascript:;" onclick="scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>

!Licence and Copyright
Copyright (c) abego Software ~GmbH, 2006 ([[www.abego-software.de|http://www.abego-software.de]])

Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this
list of conditions and the following disclaimer in the documentation and/or other
materials provided with the distribution.

Neither the name of abego Software nor the names of its contributors may be
used to endorse or promote products derived from this software without specific
prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
DAMAGE.

<html><sub><a href="javascript:;" onclick="scrollAnchorVisible('Top',null, event)">[Top]</sub></a></html>
***/

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>

<part LQ hidden>
Leading Question:  
How does the revenue collected by the government vary with the tax rate?
</part>

<part data hidden>
Economist Arthur Laffer introduced the idea that decreasing a tax rate can actually lead to an increase in government revenue.  The theory is that people will work harder and earn more money if they are taxed at a lower rate, so the government ends up with more revenue than it would at a higher rate.

There is much disagreement among economists about the specific shape of Laffer curves depicting government revenue $y$ versus tax rate $x$.

Two plausible curves are $$y=x(100-x)(x^2+500)$$
and $$y = \frac{300x-3x^2}{5x+100}.$$

The domain in each case is $0 \le x \le 100.$

</part>

/***
|''Name:''|ProcessingPlugin|
|''Description:''|TiddlyWiki Bundle of John Ressig's processing.js|
|''Date:''|May 9, 2008|
|''Author:''|PaulDowney (psd (at) osmosoft (dot) com)|
|''CodeRepository:''|http://svn.tiddlywiki.org/Trunk/contributors/PaulDowney/plugins/ProcessingPlugin.js|
|''Version:''|0.2|
|''License:''|[[MIT license]]|
|''Comments:''|Please make comments at http://groups.google.co.uk/group/TiddlyWikiDev |
|''~CoreVersion:''|2.2|

With contributions from Simon Baird.

***/

//{{{

// Ensure Plugin is only installed once.
if(!version.extensions.Processingjs) {
version.extensions.Processingjs = {installed:true};

config.macros.Processing = {
	counter: 0,
	handler: function (place,macroName,params,wikifier,paramString,tiddler) {
		var id = "processingcanvas"+this.counter;
		var canvas = createTiddlyElement(place,"canvas",id);

		// inlined code
		var code = paramString;

		// quick and dirty grab of code from a named tiddler
		if (store.tiddlerExists(params[0])) {
			code = store.getTiddlerText(params[0]);
		}

		// or with no params, grab code from this tiddler
		if (paramString.trim() == '') {
			code = tiddler.text;
		}

		createTiddlyElement(place,"br");
		var restartBtn = createTiddlyButton(place,"restart","restart",function() {
				story.refreshTiddler(tiddler.title,null,true);
				return false;
			},
			'processingRestart' // it's a class so you can style the button
		);

		Processing(canvas,code);
	}
};

// requires 2.4
merge(config.macros.view.views,{
	processing: function(value,place,params,wikifier,paramString,tiddler) {
		wikify("<<Processing\n"+value+"\n>>",place,highlightHack,tiddler);
	}
});

/*
 *  inlined copy of Processing.js
 *  latest code at: http://ejohn.org/blog/processingjs/
 */

/*
 * Processing.js - John Resig (http://ejohn.org/)
 * MIT Licensed
 * http://ejohn.org/blog/processingjs/
 *
 * This is a port of the Processing Visualization Language.
 * More information: http://processing.org/
 */

(function(){

this.Processing = function Processing( aElement, aCode )
{
  var p = buildProcessing( aElement );
  p.init( aCode );
  return p;
};

function log()
{
  try
  {
    console.log.apply( console, arguments );
  }
  catch(e)
  {
    try
    {
      opera.postError.apply( opera, arguments );
    }
    catch(e){}
  }
}

function parse( aCode, p )
{
  // Angels weep at this parsing code :-(

  // Remove end-of-line comments
  aCode = aCode.replace(/\/\/ .*\n/g, "\n");

  // Weird parsing errors with %
  aCode = aCode.replace(/([^\s])%([^\s])/g, "$1 % $2");
 
  // Simple convert a function-like thing to function
  aCode = aCode.replace(/(?:static )?(\w+ )(\w+)\s*(\([^\)]*\)\s*{)/g, function(all, type, name, args)
  {
    if ( name == "if" || name == "for" || name == "while" )
    {
      return all;
    }
    else
    {
      return "Processing." + name + " = function " + name + args;
    }
  });

  // Force .length() to be .length
  aCode = aCode.replace(/\.length\(\)/g, ".length");

  // foo( int foo, float bar )
  aCode = aCode.replace(/([\(,]\s*)(\w+)((?:\[\])+| )\s*(\w+\s*[\),])/g, "$1$4");
  aCode = aCode.replace(/([\(,]\s*)(\w+)((?:\[\])+| )\s*(\w+\s*[\),])/g, "$1$4");

  // float[] foo = new float[5];
  aCode = aCode.replace(/new (\w+)((?:\[([^\]]*)\])+)/g, function(all, name, args)
  {
    return "new ArrayList(" + args.slice(1,-1).split("][").join(", ") + ")";
  });
  
  aCode = aCode.replace(/(?:static )?\w+\[\]\s*(\w+)\[?\]?\s*=\s*{.*?};/g, function(all)
  {
    return all.replace(/{/g, "[").replace(/}/g, "]");
  });

  // int|float foo;
  var intFloat = /(\n\s*(?:int|float)(?:\[\])?(?:\s*|[^\(]*?,\s*))([a-z]\w*)(;|,)/i;
  while ( intFloat.test(aCode) )
  {
    aCode = aCode.replace(new RegExp(intFloat), function(all, type, name, sep)
    {
      return type + " " + name + " = 0" + sep;
    });
  }

  // float foo = 5;
  aCode = aCode.replace(/(?:static )?(\w+)((?:\[\])+| ) *(\w+)\[?\]?(\s*[=,;])/g, function(all, type, arr, name, sep)
  {
    if ( type == "return" )
      return all;
    else
      return "var " + name + sep;
  });

  // Fix Array[] foo = {...} to [...]
  aCode = aCode.replace(/=\s*{((.|\s)*?)};/g, function(all,data)
  {
    return "= [" + data.replace(/{/g, "[").replace(/}/g, "]") + "]";
  });
  
  // static { ... } blocks
  aCode = aCode.replace(/static\s*{((.|\n)*?)}/g, function(all, init)
  {
    // Convert the static definitons to variable assignments
    //return init.replace(/\((.*?)\)/g, " = $1");
    return init;
  });

  // super() is a reserved word
  aCode = aCode.replace(/super\(/g, "superMethod(");

  var classes = ["int", "float", "boolean", "string"];

  function ClassReplace(all, name, extend, vars, last)
  {
    classes.push( name );

    var static = "";

    vars = vars.replace(/final\s+var\s+(\w+\s*=\s*.*?;)/g, function(all,set)
    {
      static += " " + name + "." + set;
      return "";
    });

    // Move arguments up from constructor and wrap contents with
    // a with(this), and unwrap constructor
    return "function " + name + "() {with(this){\n  " +
      (extend ? "var __self=this;function superMethod(){extendClass(__self,arguments," + extend + ");}\n" : "") +
      // Replace var foo = 0; with this.foo = 0;
      // and force var foo; to become this.foo = null;
      vars
        .replace(/,\s?/g, ";\n  this.")
        .replace(/\b(var |final |public )+\s*/g, "this.")
        .replace(/this.(\w+);/g, "this.$1 = null;") + 
	(extend ? "extendClass(this, " + extend + ");\n" : "") +
        "<CLASS " + name + " " + static + ">" + (typeof last == "string" ? last : name + "(");
  }

  var matchClasses = /(?:public |abstract |static )*class (\w+)\s*(?:extends\s*(\w+)\s*)?{\s*((?:.|\n)*?)\b\1\s*\(/g;
  var matchNoCon = /(?:public |abstract |static )*class (\w+)\s*(?:extends\s*(\w+)\s*)?{\s*((?:.|\n)*?)(Processing)/g;
  
  aCode = aCode.replace(matchClasses, ClassReplace);
  aCode = aCode.replace(matchNoCon, ClassReplace);

  var matchClass = /<CLASS (\w+) (.*?)>/, m;
  
  while ( (m = aCode.match( matchClass )) )
  {
    var left = RegExp.leftContext,
      allRest = RegExp.rightContext,
      rest = nextBrace(allRest),
      className = m[1],
      staticVars = m[2] || "";
      
    allRest = allRest.slice( rest.length + 1 );

    rest = rest.replace(new RegExp("\\b" + className + "\\(([^\\)]*?)\\)\\s*{", "g"), function(all, args)
    {
      args = args.split(/,\s*?/);
      
      if ( args[0].match(/^\s*$/) )
        args.shift();
      
      var fn = "if ( arguments.length == " + args.length + " ) {\n";
        
      for ( var i = 0; i < args.length; i++ )
      {
        fn += "    var " + args[i] + " = arguments[" + i + "];\n";
      }
        
      return fn;
    });
    
    // Fix class method names
    // this.collide = function() { ... }
    // and add closing } for with(this) ...
    rest = rest.replace(/(?:public )?Processing.\w+ = function (\w+)\((.*?)\)/g, function(all, name, args)
    {
      return "ADDMETHOD(this, '" + name + "', function(" + args + ")";
    });
    
    var matchMethod = /ADDMETHOD([\s\S]*?{)/, mc;
    var methods = "";
    
    while ( (mc = rest.match( matchMethod )) )
    {
      var prev = RegExp.leftContext,
        allNext = RegExp.rightContext,
        next = nextBrace(allNext);

      methods += "addMethod" + mc[1] + next + "});"
      
      rest = prev + allNext.slice( next.length + 1 );
      
    }

    rest = methods + rest;
    
    aCode = left + rest + "\n}}" + staticVars + allRest;
  }

  // Do some tidying up, where necessary
  aCode = aCode.replace(/Processing.\w+ = function addMethod/g, "addMethod");
  
  function nextBrace( right )
  {
    var rest = right;
    var position = 0;
    var leftCount = 1, rightCount = 0;
    
    while ( leftCount != rightCount )
    {
      var nextLeft = rest.indexOf("{");
      var nextRight = rest.indexOf("}");
      
      if ( nextLeft < nextRight && nextLeft != -1 )
      {
        leftCount++;
        rest = rest.slice( nextLeft + 1 );
        position += nextLeft + 1;
      }
      else
      {
        rightCount++;
        rest = rest.slice( nextRight + 1 );
        position += nextRight + 1;
      }
    }
    
    return right.slice(0, position - 1);
  }

  // Handle (int) Casting
  aCode = aCode.replace(/\(int\)/g, "0|");

  // Remove Casting
  aCode = aCode.replace(new RegExp("\\((" + classes.join("|") + ")(\\[\\])?\\)", "g"), "");
  
  // Convert 3.0f to just 3.0
  aCode = aCode.replace(/(\d+)f/g, "$1");

  // Force numbers to exist
  //aCode = aCode.replace(/([^.])(\w+)\s*\+=/g, "$1$2 = ($2||0) +");

  // Force characters-as-bytes to work
  aCode = aCode.replace(/('[a-zA-Z0-9]')/g, "$1.charCodeAt(0)");

  // Convert #aaaaaa into color
  aCode = aCode.replace(/#([a-f0-9]{6})/ig, function(m, hex){
    var num = toNumbers(hex);
    return "color(" + num[0] + "," + num[1] + "," + num[2] + ")";
  });

  function toNumbers( str ){
    var ret = [];
     str.replace(/(..)/g, function(str){
      ret.push( parseInt( str, 16 ) );
    });
    return ret;
  }

//log(aCode);

  return aCode;
}

function buildProcessing( curElement ){

  var p = {};

  // init
  p.PI = Math.PI;
  p.TWO_PI = 2 * p.PI;
  p.HALF_PI = p.PI / 2;
  p.P3D = 3;
  p.CORNER = 0;
  p.CENTER = 1;
  p.CENTER_RADIUS = 2;
  p.RADIUS = 2;
  p.POLYGON = 1;
  p.TRIANGLES = 6;
  p.POINTS = 7;
  p.LINES = 8;
  p.TRIANGLE_STRIP = 9;
  p.CORNERS = 10;
  p.CLOSE = true;
  p.RGB = 1;
  p.HSB = 2;

  // "Private" variables used to maintain state
  var curContext = curElement.getContext("2d");
  var doFill = true;
  var doStroke = true;
  var loopStarted = false;
  var hasBackground = false;
  var doLoop = true;
  var curRectMode = p.CORNER;
  var curEllipseMode = p.CENTER;
  var inSetup = false;
  var inDraw = false;
  var curBackground = "rgba(204,204,204,1)";
  var curFrameRate = 1000;
  var curShape = p.POLYGON;
  var curShapeCount = 0;
  var opacityRange = 255;
  var redRange = 255;
  var greenRange = 255;
  var blueRange = 255;
  var pathOpen = false;
  var mousePressed = false;
  var keyPressed = false;
  var firstX, firstY, prevX, prevY;
  var curColorMode = p.RGB;
  var curTint = -1;
  var curTextSize = 12;
  var curTextFont = "Arial";
  var getLoaded = false;
  var start = (new Date).getTime();

  // Global vars for tracking mouse position
  p.pmouseX = 0;
  p.pmouseY = 0;
  p.mouseX = 0;
  p.mouseY = 0;

  // Will be replaced by the user, most likely
  p.mouseDragged = undefined;
  p.mouseMoved = undefined;
  p.mousePressed = undefined;
  p.mouseReleased = undefined;
  p.keyPressed = undefined;
  p.keyReleased = undefined;
  p.draw = undefined;
  p.setup = undefined;

  // The height/width of the canvas
  p.width = curElement.width - 0;
  p.height = curElement.height - 0;
  
  // In case I ever need to do HSV conversion:
  // http://srufaculty.sru.edu/david.dailey/javascript/js/5rml.js
  p.color = function color( aValue1, aValue2, aValue3, aValue4 )
  {
    var aColor = "";
    
    if ( arguments.length == 3 )
    {
      aColor = p.color( aValue1, aValue2, aValue3, opacityRange );
    }
    else if ( arguments.length == 4 )
    {
      var a = aValue4 / opacityRange;
      a = isNaN(a) ? 1 : a;

      if ( curColorMode == p.HSB )
      {
        var rgb = HSBtoRGB(aValue1, aValue2, aValue3);
        var r = rgb[0], g = rgb[1], b = rgb[2];
      }
      else
      {
        var r = getColor(aValue1, redRange);
        var g = getColor(aValue2, greenRange);
        var b = getColor(aValue3, blueRange);
      }

      aColor = "rgba(" + r + "," + g + "," + b + "," + a + ")";
    }
    else if ( typeof aValue1 == "string" )
    {
      aColor = aValue1;

      if ( arguments.length == 2 )
      {
        var c = aColor.split(",");
	c[3] = (aValue2 / opacityRange) + ")";
	aColor = c.join(",");
      }
    }
    else if ( arguments.length == 2 )
    {
      aColor = p.color( aValue1, aValue1, aValue1, aValue2 );
    }
    else if ( typeof aValue1 == "number" )
    {
      aColor = p.color( aValue1, aValue1, aValue1, opacityRange );
    }
    else
    {
      aColor = p.color( redRange, greenRange, blueRange, opacityRange );
    }

    // HSB conversion function from Mootools, MIT Licensed
    function HSBtoRGB(h, s, b)
    {
      h = (h / redRange) * 100;
      s = (s / greenRange) * 100;
      b = (b / blueRange) * 100;
      if (s == 0){
        return [b, b, b];
      } else {
        var hue = h % 360;
        var f = hue % 60;
        var br = Math.round(b / 100 * 255);
        var p = Math.round((b * (100 - s)) / 10000 * 255);
        var q = Math.round((b * (6000 - s * f)) / 600000 * 255);
        var t = Math.round((b * (6000 - s * (60 - f))) / 600000 * 255);
        switch (Math.floor(hue / 60)){
          case 0: return [br, t, p];
          case 1: return [q, br, p];
          case 2: return [p, br, t];
          case 3: return [p, q, br];
          case 4: return [t, p, br];
          case 5: return [br, p, q];
        }
      }
    }

    function getColor( aValue, range )
    {
      return Math.round(255 * (aValue / range));
    }
    
    return aColor;
  }

  p.nf = function( num, pad )
  {
    var str = "" + num;
    while ( pad - str.length )
      str = "0" + str;
    return str;
  };

  p.AniSprite = function( prefix, frames )
  {
    this.images = [];
    this.pos = 0;

    for ( var i = 0; i < frames; i++ )
    {
      this.images.push( prefix + p.nf( i, ("" + frames).length ) + ".gif" );
    }

    this.display = function( x, y )
    {
      p.image( this.images[ this.pos ], x, y );

      if ( ++this.pos >= frames )
        this.pos = 0;
    };

    this.getWidth = function()
    {
      return getImage(this.images[0]).width;
    };

    this.getHeight = function()
    {
      return getImage(this.images[0]).height;
    };
  };

  function buildImageObject( obj )
  {
    var pixels = obj.data;
    var data = p.createImage( obj.width, obj.height );

    if ( data.__defineGetter__ && data.__lookupGetter__ && !data.__lookupGetter__("pixels") )
    {
      var pixelsDone;
      data.__defineGetter__("pixels", function()
      {
        if ( pixelsDone )
	  return pixelsDone;

	pixelsDone = [];

        for ( var i = 0; i < pixels.length; i += 4 )
        {
          pixelsDone.push( p.color(pixels[i], pixels[i+1], pixels[i+2], pixels[i+3]) );
        }

	return pixelsDone;
      });
    }
    else
    {
      data.pixels = [];

      for ( var i = 0; i < pixels.length; i += 4 )
      {
        data.pixels.push( p.color(pixels[i], pixels[i+1], pixels[i+2], pixels[i+3]) );
      }
    }

    return data;
  }

  p.createImage = function createImage( w, h, mode )
  {
    var data = {
      width: w,
      height: h,
      pixels: new Array( w * h ),
      get: function(x,y)
      {
        return this.pixels[w*y+x];
      },
      _mask: null,
      mask: function(img)
      {
        this._mask = img;
      },
      loadPixels: function()
      {
      },
      updatePixels: function()
      {
      }
    };

    return data;
  }

  p.createGraphics = function createGraphics( w, h )
  {
    var canvas = document.createElement("canvas");
    var ret = buildProcessing( canvas );
    ret.size( w, h );
    ret.canvas = canvas;
    return ret;
  }

  p.beginDraw = function beginDraw()
  {

  }

  p.endDraw = function endDraw()
  {

  }

  p.tint = function tint( rgb, a )
  {
    curTint = a;
  }

  function getImage( img ) {
    if ( typeof img == "string" )
    {
      return document.getElementById(img);
    }

    if ( img.img || img.canvas )
    {
      return img.img || img.canvas;
    }

    img.data = [];

    for ( var i = 0, l = img.pixels.length; i < l; i++ )
    {
      var c = (img.pixels[i] || "rgba(0,0,0,1)").slice(5,-1).split(",");
      img.data.push( parseInt(c[0]), parseInt(c[1]), parseInt(c[2]), parseFloat(c[3]) * 100 );
    }

    var canvas = document.createElement("canvas")
    canvas.width = img.width;
    canvas.height = img.height;
    var context = canvas.getContext("2d");
    context.putImageData( img, 0, 0 );

    img.canvas = canvas;

    return canvas;
  }

  p.image = function image( img, x, y, w, h )
  {
    x = x || 0;
    y = y || 0;

    var obj = getImage(img);

    if ( curTint >= 0 )
    {
      var oldAlpha = curContext.globalAlpha;
      curContext.globalAlpha = curTint / opacityRange;
    }

    if ( arguments.length == 3 )
    {
      curContext.drawImage( obj, x, y );
    }
    else
    {
      curContext.drawImage( obj, x, y, w, h );
    }

    if ( curTint >= 0 )
    {
      curContext.globalAlpha = oldAlpha;
    }

    if ( img._mask )
    {
      var oldComposite = curContext.globalCompositeOperation;
      curContext.globalCompositeOperation = "darker";
      p.image( img._mask, x, y );
      curContext.globalCompositeOperation = oldComposite;
    }
  }

  p.exit = function exit()
  {

  }

  p.save = function save( file )
  {

  }

  p.loadImage = function loadImage( file )
  {
    var img = document.getElementById(file);
    if ( !img )
      return;

    var h = img.height, w = img.width;

    var canvas = document.createElement("canvas");
    canvas.width = w;
    canvas.height = h;
    var context = canvas.getContext("2d");

    context.drawImage( img, 0, 0 );
    var data = buildImageObject( context.getImageData( 0, 0, w, h ) );
    data.img = img;
    return data;
  }

  p.loadFont = function loadFont( name )
  {
    return {
      name: name,
      width: function( str )
      {
        if ( curContext.mozMeasureText )
          return curContext.mozMeasureText( typeof str == "number" ?
            String.fromCharCode( str ) :
            str) / curTextSize;
	else
	  return 0;
      }
    };
  }

  p.textFont = function textFont( name, size )
  {
    curTextFont = name;
    p.textSize( size );
  }

  p.textSize = function textSize( size )
  {
    if ( size )
    {
      curTextSize = size;
    }
  }

  p.textAlign = function textAlign()
  {

  }

  p.text = function text( str, x, y )
  {
    if ( str && curContext.mozDrawText )
    {
      curContext.save();
      curContext.mozTextStyle = curTextSize + "px " + curTextFont.name;
      curContext.translate(x, y);
      curContext.mozDrawText( typeof str == "number" ?
        String.fromCharCode( str ) :
	str );
      curContext.restore();
    }
  }

  p.char = function char( key )
  {
    //return String.fromCharCode( key );
    return key;
  }

  p.println = function println()
  {

  }

  p.map = function map( value, istart, istop, ostart, ostop )
  {
    return ostart + (ostop - ostart) * ((value - istart) / (istop - istart));
  };

  String.prototype.replaceAll = function(re, replace)
  {
    return this.replace(new RegExp(re, "g"), replace);
  };

  p.Point = function Point( x, y )
  {
    this.x = x;
    this.y = y;
    this.copy = function()
    {
      return new Point( x, y );
    }
  }

  p.Random = function()
  {
    var haveNextNextGaussian = false;
    var nextNextGaussian;

    this.nextGaussian = function()
    {
      if (haveNextNextGaussian) {
        haveNextNextGaussian = false;

        return nextNextGaussian;
      } else {
        var v1, v2, s;
        do { 
          v1 = 2 * p.random(1) - 1;   // between -1.0 and 1.0
          v2 = 2 * p.random(1) - 1;   // between -1.0 and 1.0
          s = v1 * v1 + v2 * v2;
        } while (s >= 1 || s == 0);
        var multiplier = Math.sqrt(-2 * Math.log(s)/s);
        nextNextGaussian = v2 * multiplier;
        haveNextNextGaussian = true;

        return v1 * multiplier;
      }
    };
  }

  p.ArrayList = function ArrayList( size, size2, size3 )
  {
    var array = new Array( 0 | size );
    
    if ( size2 )
    {
      for ( var i = 0; i < size; i++ )
      {
        array[i] = [];

        for ( var j = 0; j < size2; j++ )
        {
	  var a = array[i][j] = size3 ? new Array( size3 ) : 0;
	  for ( var k = 0; k < size3; k++ )
	  {
	    a[k] = 0;
	  }
        }
      }
    }
    else
    {
      for ( var i = 0; i < size; i++ )
      {
        array[i] = 0;
      }
    }
    
    array.size = function()
    {
      return this.length;
    };
    array.get = function( i )
    {
      return this[ i ];
    };
    array.remove = function( i )
    {
      return this.splice( i, 1 );
    };
    array.add = function( item )
    {
      for ( var i = 0; this[ i ] != undefined; i++ ) {}
      this[ i ] = item;
    };
    array.clone = function()
    {
      var a = new ArrayList( size );
      for ( var i = 0; i < size; i++ )
      {
        a[ i ] = this[ i ];
      }
      return a;
    };
    array.isEmpty = function()
    {
      return !this.length;
    };
    array.clear = function()
    {
      this.length = 0;
    };
    
    return array;
  }
  
  p.colorMode = function colorMode( mode, range1, range2, range3, range4 )
  {
    curColorMode = mode;

    if ( arguments.length >= 4 )
    {
      redRange = range1;
      greenRange = range2;
      blueRange = range3;
    }

    if ( arguments.length == 5 )
    {
      opacityRange = range4;
    }

    if ( arguments.length == 2 )
    {
      p.colorMode( mode, range1, range1, range1, range1 );
    }
  }
  
  p.beginShape = function beginShape( type )
  {
    curShape = type;
    curShapeCount = 0; 
  }
  
  p.endShape = function endShape( close )
  {
    if ( curShapeCount != 0 )
    {
      curContext.lineTo( firstX, firstY );

      if ( doFill )
        curContext.fill();
        
      if ( doStroke )
        curContext.stroke();
    
      curContext.closePath();
      curShapeCount = 0;
      pathOpen = false;
    }

    if ( pathOpen )
    {
      curContext.closePath();
    }
  }
  
  p.vertex = function vertex( x, y, x2, y2, x3, y3 )
  {
    if ( curShapeCount == 0 && curShape != p.POINTS )
    {
      pathOpen = true;
      curContext.beginPath();
      curContext.moveTo( x, y );
    }
    else
    {
      if ( curShape == p.POINTS )
      {
        p.point( x, y );
      }
      else if ( arguments.length == 2 )
      {
        if ( curShape == p.TRIANGLE_STRIP && curShapeCount == 2 )
	{
          curContext.moveTo( prevX, prevY );
          curContext.lineTo( firstX, firstY );
	}

        curContext.lineTo( x, y );
      }
      else if ( arguments.length == 4 )
      {
        if ( curShapeCount > 1 )
        {
	  curContext.moveTo( prevX, prevY );
          curContext.quadraticCurveTo( firstX, firstY, x, y );
	  curShapeCount = 1;
        }
      }
      else if ( arguments.length == 6 )
      {
        curContext.bezierCurveTo( x, y, x2, y2, x3, y3 );
        curShapeCount = -1;
      }
    }

    prevX = firstX;
    prevY = firstY;
    firstX = x;
    firstY = y;

    
    curShapeCount++;
    
    if ( curShape == p.LINES && curShapeCount == 2 ||
         (curShape == p.TRIANGLES || curShape == p.TRIANGLE_STRIP) && curShapeCount == 3 )
    {
      p.endShape();
    }

    if ( curShape == p.TRIANGLE_STRIP && curShapeCount == 3 )
    {
      curShapeCount = 2;
    }
  }

  p.curveTightness = function()
  {

  }

  // Unimplmented - not really possible with the Canvas API
  p.curveVertex = function( x, y, x2, y2 )
  {
    p.vertex( x, y, x2, y2 );
  }

  p.bezierVertex = p.vertex
  
  p.rectMode = function rectMode( aRectMode )
  {
    curRectMode = aRectMode;
  }

  p.imageMode = function()
  {

  }
  
  p.ellipseMode = function ellipseMode( aEllipseMode )
  {
    curEllipseMode = aEllipseMode;
  }
  
  p.dist = function dist( x1, y1, x2, y2 )
  {
    return Math.sqrt( Math.pow( x2 - x1, 2 ) + Math.pow( y2 - y1, 2 ) );
  }

  p.year = function year()
  {
    return (new Date).getYear() + 1900;
  }

  p.month = function month()
  {
    return (new Date).getMonth();
  }

  p.day = function day()
  {
    return (new Date).getDay();
  }

  p.hour = function hour()
  {
    return (new Date).getHours();
  }

  p.minute = function minute()
  {
    return (new Date).getMinutes();
  }

  p.second = function second()
  {
    return (new Date).getSeconds();
  }

  p.millis = function millis()
  {
    return (new Date).getTime() - start;
  }
  
  p.ortho = function ortho()
  {
  
  }
  
  p.translate = function translate( x, y )
  {
    curContext.translate( x, y );
  }
  
  p.scale = function scale( x, y )
  {
    curContext.scale( x, y || x );
  }
  
  p.rotate = function rotate( aAngle )
  {
    curContext.rotate( aAngle );
  }
  
  p.pushMatrix = function pushMatrix()
  {
    curContext.save();
  }
  
  p.popMatrix = function popMatrix()
  {
    curContext.restore();
  }
  
  p.redraw = function redraw()
  {
    if ( hasBackground )
    {
      p.background();
    }
    
    inDraw = true;
    p.pushMatrix();
    p.draw();
    p.popMatrix();
    inDraw = false;
  }
  
  p.loop = function loop()
  {
    if ( loopStarted )
      return;
    
    var looping = setInterval(function()
    {
      try
      {
        p.redraw();
      }
      catch(e)
      {
        clearInterval( looping );
        throw e;
      }
    }, 1000 / curFrameRate );
    
    loopStarted = true;
  }
  
  p.frameRate = function frameRate( aRate )
  {
    curFrameRate = aRate;
  }
  
  p.background = function background( img )
  {
    if ( arguments.length )
    {
      if ( img && img.img )
      {
        curBackground = img;
      }
      else
      {
        curBackground = p.color.apply( this, arguments );
      }
    }
    

    if ( curBackground.img )
    {
      p.image( curBackground, 0, 0 );
    }
    else
    {
      var oldFill = curContext.fillStyle;
      curContext.fillStyle = curBackground + "";
      curContext.fillRect( 0, 0, p.width, p.height );
      curContext.fillStyle = oldFill;
    }
  }

  p.sq = function sq( aNumber )
  {
    return aNumber * aNumber;
  }

  p.sqrt = function sqrt( aNumber )
  {
    return Math.sqrt( aNumber );
  }
  
  p.int = function int( aNumber )
  {
    return Math.floor( aNumber );
  }

  p.min = function min( aNumber, aNumber2 )
  {
    return Math.min( aNumber, aNumber2 );
  }

  p.max = function max( aNumber, aNumber2 )
  {
    return Math.max( aNumber, aNumber2 );
  }

  p.ceil = function ceil( aNumber )
  {
    return Math.ceil( aNumber );
  }

  p.floor = function floor( aNumber )
  {
    return Math.floor( aNumber );
  }

  p.float = function float( aNumber )
  {
    return typeof aNumber == "string" ?
	p.float( aNumber.charCodeAt(0) ) :
        parseFloat( aNumber );
  }

  p.byte = function byte( aNumber )
  {
    return aNumber || 0;
  }
  
  p.random = function random( aMin, aMax )
  {
    return arguments.length == 2 ?
      aMin + (Math.random() * (aMax - aMin)) :
      Math.random() * aMin;
  }

  // From: http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
  p.noise = function( x, y, z )
  {
    return arguments.length >= 2 ?
      PerlinNoise_2D( x, y ) :
      PerlinNoise_2D( x, x );
  }

  function Noise(x, y)
  {
    var n = x + y * 57;
    n = (n<<13) ^ n;
    return Math.abs(1.0 - (((n * ((n * n * 15731) + 789221) + 1376312589) & 0x7fffffff) / 1073741824.0));
  }

  function SmoothedNoise(x, y)
  {
    var corners = ( Noise(x-1, y-1)+Noise(x+1, y-1)+Noise(x-1, y+1)+Noise(x+1, y+1) ) / 16;
    var sides   = ( Noise(x-1, y)  +Noise(x+1, y)  +Noise(x, y-1)  +Noise(x, y+1) ) /  8;
    var center  =  Noise(x, y) / 4;
    return corners + sides + center;
  }

  function InterpolatedNoise(x, y)
  {
    var integer_X    = Math.floor(x);
    var fractional_X = x - integer_X;

    var integer_Y    = Math.floor(y);
    var fractional_Y = y - integer_Y;

    var v1 = SmoothedNoise(integer_X,     integer_Y);
    var v2 = SmoothedNoise(integer_X + 1, integer_Y);
    var v3 = SmoothedNoise(integer_X,     integer_Y + 1);
    var v4 = SmoothedNoise(integer_X + 1, integer_Y + 1);

    var i1 = Interpolate(v1 , v2 , fractional_X);
    var i2 = Interpolate(v3 , v4 , fractional_X);

    return Interpolate(i1 , i2 , fractional_Y);
  }

  function PerlinNoise_2D(x, y)
  {
      var total = 0;
      var p = 0.25;
      var n = 3;

      for ( var i = 0; i <= n; i++ )
      {
          var frequency = Math.pow(2, i);
          var amplitude = Math.pow(p, i);

          total = total + InterpolatedNoise(x * frequency, y * frequency) * amplitude;
      }

      return total;
  }

  function Interpolate(a, b, x)
  {
    var ft = x * p.PI;
    var f = (1 - p.cos(ft)) * .5;
    return  a*(1-f) + b*f;
  }

  p.red = function( aColor )
  {
    return parseInt(aColor.slice(5));
  }

  p.green = function( aColor )
  {
    return parseInt(aColor.split(",")[1]);
  }

  p.blue = function( aColor )
  {
    return parseInt(aColor.split(",")[2]);
  }

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})();


} //# end of "install only once"
//}}}

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
Outline "Outline" ./outline
>>
<<tiddler [[LGR]]>>

<part outline hidden>
*Definition of function
*Domain and range
*Numeric, symbolic, and graphic representations
*Domain convention
*Function evaluation
*Vertical line test
</part>

<part LQ hidden>
Leading Question:  
How has the number of internet users worldwide changed with time, and what does this indicate for future use of the internet?
</part>

<part data hidden>
The following table shows the estimated number of Internet users worldwide from 1995-2006, according to www.internetworldstats.com

| Year | Millions of Users |
| 1995 | 16 |
| 1996 | 36 |
| 1997 | 101 |
| 1998 | 150 |
| 1999 | 250 |
| 2000 | 451 |
| 2001 | 553 |
| 2002 | 587 |
| 2003 | 719 |
| 2004 | 817 |
| 2005 | 1018 |
| 2006 | 1043 |

</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
Outline "Outline" ./outline
>>
<<tiddler [[LGR]]>>

<part outline hidden>
*Definition of quadratic function
*Graphing quadratic functions by elementary transformations
*Identifying the vertex from the form $y=a(x-h)^2+k$
*Completing the square
*Identifying the vertex from the form $y=ax^2+bx+c$
</part>

<part LQ hidden>
Leading Question:  
How much should a company charge for its seminars?
</part>

<part data hidden>
When Power and Money, Inc., charges 600 dollars for a seminar on management techniques, it attracts 1000 people.  For each 20 dollar decrease in the fee, an additional 100 people will attend the seminar.

The managers wonder how much to charge for the seminar to maximize their revenue.

</part>

*Fall 2009
**[[Quiz 1|quizzes/mat-151-012-2009-fall-quiz-1.pdf]]
**[[Quiz 2|quizzes/mat-151-012-2009-fall-quiz-2.pdf]]
**[[Quiz 3|quizzes/mat-151-012-2009-fall-quiz-3.pdf]]
**[[Quiz 4|quizzes/mat-151-012-2009-fall-quiz-4.pdf]]
**[[Quiz 5|quizzes/mat-151-012-2009-fall-quiz-5.pdf]] | [[Solutions|quizzes/mat-151-012-2009-fall-quiz-5-solutions.pdf]]

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
How does the manufacturing cost of a DVD change as the number of ~DVDs manufactured changes?
</part>

<part data hidden>
Suppose that the cost of manufacturing $x$ cases of a DVD title is given by
$$C(x) = 100 +15x - x^2$$
where $0 \le x \le 7.$
</part>

<<tabs Examples
Strategy "Strategy" ./strategy
Problem1 "Problem" ./relatedrate1
Problem2 "Problem" ./relatedrate2
Problem3 "Problem" ./relatedrate3
>>

/%
<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>
%/

<part LQ hidden>
Leading Question:  
When a skier's blood vessels contract because of the cold, how fast is the velocity of blood changing?
</part>

<part data hidden>
Assume Poiseuille's law for blood flow in the form
$$V = k(R^2 - r^2),$$
where $V$ is the velocity of blood, $R$ is the radius of the blood vessell, and $r$ is the distance of a layer of blood flow from the center of the vessel.

Take $k=375,$ treat $r$ as constant, and suppose $R=0.08$ mm at some point in time for which $\frac{dR}{dt} = -0.01$ mm/min.
</part>

<part strategy hidden>
Solving a Related Rates Problem

#Read the problem carefully.
#Draw a diagram if possible.
#Introduce notation.  Assign symbols to all quantities that are functions of time.
#Express the given information and the required rate in terms of derivatives.
#Write an equation that relates the various quantities of the problem. If necessary, eliminate one of the variables by substitution.
#Use the Chain Rule to differentiate both sides of the equation with respect to $t.$
#Substitute the given information into the resulting equation and solve for the unknown rate.
</part>

<part relatedrate1 hidden>
When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 centimeters per minute.  At what rate is the plate's area increasing when the radius is 50 centimeters?
</part>

<part relatedrate2 hidden>
A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 feet above the bow.  The rope is hauled in at the rate of 2 feet per second.  How fast is the boat approaching the dock when 10 feet of rope are out?
</part>

<part relatedrate3 hidden>
A police cruiser, approaching a right-angled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 miles per hour.  If the cruiser is moving at 60 miles per hour at the  instant of measurement, what is the speed of the car?
</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
In a 30-second commercial, when is the best time to present the sales message?
</part>

<part data hidden>
Model viewer's attention for $0 \le t \le 30$ by $$f(t) = - \frac{3}{20} t^2 + 6t + 20.$$
</part>

!Fall 2009
<<tabs Schedule
Nov "November" [[Schedule/November]]
Dec "December" [[Schedule/December]]
Aug "August" [[Schedule/August]]
Sep "September" [[Schedule/September]]
Oct "October" [[Schedule/October]]
>>
<part August hidden>
*Thursday, August 20
**Section 1.1: [[Slopes and Equations of Lines]]
**Section 1.2: [[Linear Functions and Applications]]
*Tuesday, August 25
**Section 2.1: [[Properties of Functions]]
**Section 2.2: [[Quadratic Functions]]
*Thursday, August 27
**Section 2.3: [[Polynomial and Rational Functions]]
</part>
<part September hidden>
*Tuesday, September 01
**Section 2.4: [[Exponential Functions]]
**Section 2.5: [[Logarithmic Functions]]
*Thursday, September 03
**Section 2.6: [[Applications:  Growth and Decay; Finance]]
*Tuesday, September 08
**Section 3.1: [[Limits]]
*Thursday, September 10
**Section 3.2: [[Continuity]]
*Tuesday, September 15
**Section 3.3: [[Rates of Change]]
**Section 3.4: [[Definition of the Derivative]]
*Thursday, September 17
**Section 3.5: [[Graphical Differentiation]]
**Section 4.1: [[Techniques for Finding Derivatives]]
*Tuesday, September 22
**Review
*Thursday, September 24
**Test 1
*Tuesday, September 29
**Section 4.2: [[Derivatives of Products and Quotients]]
</part>
<part October hidden>
*Thursday, October 01
**Section 4.3: [[The Chain Rule]]
**Section 4.4: [[Derivatives of Exponential Functions]]
**Section 4.5: [[Derivatives of Logarithmic Functions]]
*Tuesday, October 06
**Fall Break
*Thursday, October 08
*Tuesday, October 13
**Section 5.1: [[Increasing and Decreasing Functions]]
*Thursday, October 15
**Section 5.2: [[Relative Extrema]]
**Section 5.3: [[Higher Derivatives and Concavity]]
*Tuesday, October 20
**Section 5.4: [[Curve Sketching]]
*Thursday, October 22
**Section 6.1: [[Absolute Extrema]]
*Tuesday, October 27
**Section 6.2: [[Applications of Extrema]]
*Thursday, October 29
**Section 6.3: [[Further Applications of Extrema]]
</part>
<part November hidden>
*Tuesday, November 03
**Review
*Thursday, November 05
**Test 2
*Tuesday, November 10
**Section 6.4: [[Implicit Differentiation]]
**Section 6.5: [[Related Rates]]
*Thursday, November 12
**Section 7.1: [[Antiderivatives]]
*Tuesday, November 17
**Section 7.2: [[Substitution]]
*Thursday, November 19
**Section 7.3: [[Area and the Definite Integral]]
*Tuesday, November 24
**Section 7.4: [[The Fundamental Theorem of Calculus]]
**Section 7.5: [[The Area Between Two Curves]]
*Thursday, November 26
**Thanksgiving Holiday
</part>
<part December hidden>
*Tuesday, December 01
**Review
*Tuesday, December 08
**Final Exam, 08:00-11:00a
</part>

<<slideShow>>



-s-
!Integration by Parts

*Recall that the product rule for differentiation states
<html>
<div class="math">
\frac{d}{dx} [ f(x)g(x) ] = f'(x)g(x) + f(x)g'(x).
</div>
</html>
*Integrating, we find that
<html>
<div class="math">
\int f(x)g'(x)dx = f(x)g(x) - \int g(x)f'(x)dx.
</div>
</html>
*Making the substitutions $u = f(x)$ and $v = g(x)$, we obtain
<html>
<div class="math">
\int u \ dv = uv - \int v \ du.
</div>
</html>



-s-
!Example

*Consider $\int x \ \sin x \ dx$.
*We must choose $u$ and $dv$ appropriately to apply the integration by parts formula.
*In this case, we may choose $u=x$ and $dv=\sin x dx$.
*Then we have 
<html>
<div class="math">
\begin{eqnarray} u & = & x & \quad & dv & = & \sin x \ dx \\
du & = & dx & \quad & v & = & -\cos x \end{eqnarray}
</div>
</html>
*It follows that <html>
<div class="math">
\begin{eqnarray} \int x \sin x \ dx & = & x \cdot -\cos x - \int -\cos x \ dx \\
& = & -x \ \cos x + \int \cos x \ dx \\
& = & -x \ \cos x + \sin x + C \end{eqnarray}
</div>
</html>



-s-
!Example

*Consider $\int x^2 \cos x \ dx$.
*In this case, we may choose $u=x^2$ and $dv=\cos x \ dx$.
*We then have 
<html>
<div class="math">
\begin{eqnarray} u & = & x^2 & \quad & dv & = & \cos x \ dx \\
du & = & 2x \ dx & \quad & v & = & \sin x \end{eqnarray}
</div>
</html>
*It follows that 
<html>
<div class="math">
\begin{eqnarray} \int x^2 \cos x \ dx & = & x^2 \cdot \sin x - \int \sin x \cdot 2x \ dx \\
& = & x^2 \sin x - 2 \int x \sin x \ dx \\
& = & x^2 \sin x - 2 [ -x \ \cos x + \sin x ] + C \\
& = & x^2 \sin x + 2x \ \cos x - 2 \sin x + C \end{eqnarray}
</div>
</html>


-s-
!Choosing Parts

Two criteria to keep in mind as you apply integration by parts:

# $v$ should be easy to find from $dv$
# the integral $\int v \ du$ should be easier to evaluate than $\int u \ dv$.

In general, choosing $u$ according to the acronym LIATE will help to satisfy the second criterion.



-s-
!LIATE

LIATE is an acronym for

<<tiddler LIATE>>

Choose for $u$ the part of the integrand that appears first in LIATE and let $dv$ be whatever is left in the integrand.

Better to choose $u$ LIATE than never!


-s-
!Example
Consider $\int \cos^{-1} x \ dx$.
*Take $u=\cos^{-1} x$.




-s-
!Example
Consider $\int e^x \ \cos x \ dx$.
*Take $u=\cos x$.



-s-
!Example
Consider $\int x \ \ln x \ dx$.
*Take $u=\ln x$.



-s-
!Example
Consider $\displaystyle \int_{0}^{\pi/2} x \ \sin x \ dx$.

[[SiteTitle]]
[[SiteSubtitle]]
[[Contact Information]]
[[Schedule]]
[[Notable Dates]]
[[Assignments]]

Basic Calculus with Applications

MAT 151

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
Outline "Outline" ./outline
>>

<<tiddler [[LGR]]>>

<part outline hidden>
*Cartesian coordinates
*Slope of a Line
*Equations of a Line
**Slope-intercept form
**Point-slope form
**General form
**Horizontal
**Vertical
*Parallel / Perpendicular Lines
*Graph of a Line
</part>
<part LQ hidden>
Leading Question:
How fast has tuition at public colleges been increasing in recent years, and how well can we predict tuition in the future?
</part>
<part data hidden>
The table lists the average annual cost (in dollars) of tuition and fees at public four-year colleges for selected years, according to the Annual Survey of Colleges 2005-2006, The College Board.

| Year | Tuition and Fees |
| 2000 | 3508 |
| 2001 | 3766 |
| 2002 | 4098 |
| 2003 | 4645 |
| 2004 | 5126 |
| 2005 | 5491 |

</part>

/* horizontal main menu */

#displayArea { margin: 1em 15.5em 0em 1em; } /* use the full horizontal width */

#topMenu { background: [[ColorPalette::PrimaryMid]]; color: [[ColorPalette::PrimaryPale]]; padding: 0.2em 0.2em 0.2em 0.5em; border-bottom: 2px solid #000000; }

#topMenu br { display: none; }

#topMenu .button, #topMenu .tiddlyLink, #topMenu a { margin-left: 0.25em; margin-right: 0.25em; padding-left: 0.5em; padding-right: 0.5em; color: [[ColorPalette::PrimaryPale]]; font-size: 1.15em; }

#topMenu .button:hover, #topMenu .tiddlyLink:hover { background: [[ColorPalette::PrimaryDark]]; }

<<tabs Examples
Set1 "Set1" ./subst1
Set2 "Set2" ./subst2
Set3 "Set3" ./subst3
>>
<part subst1 hidden>
Evaluate each indefinite integral by substitution.

# $\int 2 (2x+3)^3 dx$
# $\int (-4x+1)^4 dx$
# $\int 4(5x-4)^2 dx$
# $\int(3x^2-5)^4 2x dx$ 

</part>
<part subst2 hidden>
Evaluate each indefinite integral by substitution.

# $\int \frac{x+1}{(x^2+2x-4)^4} dx$
# $\int x^2 \sqrt{2x^3+7} dx$
# $\int \frac{x^2}{\root3{2x^3+7}} dx$
# $\int xe^{3x^2-5} dx$

</part>
<part subst3 hidden>
Evaluate each indefinite integral by substitution.

# $\int \frac{x+1}{x^2+2x-4} dx$
# $\int \frac{(1+\ln x)^2}{x} dx$
# $\int \frac{e^{2x}}{e^{2x}+2} dx$

</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Questions:  
How can a manager determine the best production level if the relationship between profit and production is known?  

How fast is the number of Americans who are expected to be over 100 years old growing?
</part>

<part data hidden>
Consider the cost function $C(q) = 2100 + 0.25q, 0 \le q \le 30000$ and demand function $p = \frac{50000-q}{25000}$ for the first question.

Consider the model $f(t) = 0.4018t^2 + 2.039t + 50.071$ for the number of Americans (in thousands) who are expected to be over 100 years old $t$ years after 1994.
</part>

*Fall 2009
**[[Test 1 Sample|tests/mat-151-012-2009-fall-test1-sample.pdf]]
**[[Test 2 Sample|tests/mat-151-012-2009-fall-test2-sample.pdf]]

<<tabs Examples
Strategy "Strategy" ./strategy
Set1 "Set1" ./area1
Set2 "Set2" ./area2
AverageValue "Average Value" ./average
>>

<part strategy hidden>
!How to find the area between two curves

#Graph the curves and draw a representative approximating rectangle.
#Find the limits $a,b$ of integration.
#Write a formula for $f(x)-g(x).$
#Integrate $[f(x)-g(x)]$ over the interval $a \le x \le b.$

</part>

<part area1 hidden>
Sketch the given region $R$ and then find its area.

# $R$ is the region bounded by the lines $y=x,$ $y=-x,$ and $x=1.$
# $R$ is the region bounded by the curves $y=x^2,$ $y=-x^2,$ and the line $x=1.$
# $R$ is the region bounded by the curves $y=x^2-2x$ and $y=-x^2+4.$

</part>
<part area2 hidden>
Sketch the given region $R$ and then find its area.

# $R$ is the region bounded by the curves $y=x^3-3x^2$ and $y=x^2+5x.$
# $R$ is the region between the curve $y=x^3$ and the line $y=9x.$
# $R$ is the region bounded by curve $y= \frac{1}{x^2}$ and the lines $y=x$ and $y=\frac{x}{8}.$

</part>
<part average hidden>
Find the average value of the given function $f(x)$ over the specified interval $a \le x \le b.$

# $f(x) = x^2 - 3x + 5$ over $-1 \le x \le 2.$
# $f(x) = 1-x^2$ over $-3 \le x \le 3.$
# $f(x) = e^{2x} + e^{-x}$ over $0 \le x \le \ln(2).$

</part>

<<tabs LQ
LQ "LQ" ./LQ
data "data" ./data
>>
<<tiddler [[LGR]]>>


<part LQ hidden>
Leading Question:  
Suppose we know how fast the radius of a circular oil slick is growing, and we know how much the area of the oil slick is growing per unit of change in the radius.  How fast is the area growing?
</part>

<part data hidden>
Let the radius (in feet) of the circular oil slick after $t$ minutes be $r(t)=4t.$  Recall that the area of circle of radius $r$ is $A(r)= \pi r^2.$
</part>

<<tabs Examples
Theorem "Theorem" ./thm
Set1 "Set1" ./definite1
Set2 "Set2" ./definite2
>>

<part thm hidden>
!The Fundamental Theorem of Calculus

If the function $f(x)$ is continuous on the interval $a \le x \le b,$ then
$$\displaystyle \int_{a}^{b} f(x) dx = F(b) - F(a)$$
where $F(x)$ is any antiderivative of $f(x)$ on $a \le x \le b.$
</part>

<part definite1 hidden>
Evaluate each definite integral using the fundamental theorem of calculus.

# $\displaystyle \int_{-1}^{2} 5 dx$
# $\displaystyle \int_{0}^{5} (3x+2) dx$
# $\displaystyle \int_{-1}^{1} 3x^4 dx$
# $\displaystyle \int_{1}^{4} 2 \sqrt{x} dx$

</part>
<part definite2 hidden>
Evaluate each definite integral using the fundamental theorem of calculus.

# $\displaystyle \int_{0}^{1} e^{-x} (4 - e^{x}) dx$
# $\displaystyle \int_{0}^{1} (x^4 + 3x^3 + 1) dx$
# $\displaystyle \int_{1}^{3} \left( 1 + \frac{1}{x} + \frac{1}{x^2} \right) dx$
# $\displaystyle \int_{1}^{2} \frac{x^2}{(x^3+1)^2} dx$

</part>

/***

|Name|ToggleSideBarMacro|
|Created by|SaqImtiaz|
|Location|http://tw.lewcid.org/#ToggleSideBarMacro|
|Version|1.0|
|Requires|~TW2.x|
!Description:
Provides a button for toggling visibility of the SideBar. You can choose whether the SideBar should initially be hidden or displayed.

!Demo
<<toggleSideBar "Toggle Sidebar">>

!Usage:
{{{<<toggleSideBar>>}}} <<toggleSideBar>>
additional options:
{{{<<toggleSideBar label tooltip show/hide>>}}} where:
label = custom label for the button,
tooltip = custom tooltip for the button,
show/hide = use one or the other, determines whether the sidebar is shown at first or not.
(default is to show the sidebar)

You can add it to your tiddler toolbar, your MainMenu, or where you like really.
If you are using a horizontal MainMenu and want the button to be right aligned, put the following in your StyleSheet:
{{{ .HideSideBarButton {float:right;} }}}

!History
*23-07-06: version 1.0: completely rewritten, now works with custom stylesheets too, and easier to customize start behaviour. 
*20-07-06: version 0.11
*27-04-06: version 0.1: working.

!Code
***/
//{{{
config.macros.toggleSideBar={};

config.macros.toggleSideBar.settings={
         styleHide :  "#sidebar { display: none;}\n"+"#contentWrapper #displayArea { margin-right: 1em;}\n"+"",
         styleShow : " ",
         arrow1: "«",
         arrow2: "»"
};

config.macros.toggleSideBar.handler=function (place,macroName,params,wikifier,paramString,tiddler)
{
          var tooltip= params[1]||'toggle sidebar';
          var mode = (params[2] && params[2]=="hide")? "hide":"show";
          var arrow = (mode == "hide")? this.settings.arrow1:this.settings.arrow2;
          var label= (params[0]&&params[0]!='.')?params[0]+" "+arrow:arrow;
          var theBtn = createTiddlyButton(place,label,tooltip,this.onToggleSideBar,"button HideSideBarButton");
          if (mode == "hide")
             { 
             (document.getElementById("sidebar")).setAttribute("toggle","hide");
              setStylesheet(this.settings.styleHide,"ToggleSideBarStyles");
             }
};

config.macros.toggleSideBar.onToggleSideBar = function(){
          var sidebar = document.getElementById("sidebar");
          var settings = config.macros.toggleSideBar.settings;
          if (sidebar.getAttribute("toggle")=='hide')
             {
              setStylesheet(settings.styleShow,"ToggleSideBarStyles");
              sidebar.setAttribute("toggle","show");
              this.firstChild.data= (this.firstChild.data).replace(settings.arrow1,settings.arrow2);
              }
          else
              {    
               setStylesheet(settings.styleHide,"ToggleSideBarStyles");
               sidebar.setAttribute("toggle","hide");
               this.firstChild.data= (this.firstChild.data).replace(settings.arrow2,settings.arrow1);
              }

     return false;
}

setStylesheet(".HideSideBarButton .button {font-weight:bold; padding: 0 5px;}\n","ToggleSideBarButtonStyles");

//}}}

**Section 1.1: [[Slopes and Equations of Lines]]
**Section 1.2: [[Linear Functions and Applications]]
**Section 2.1: [[Properties of Functions]]
**Section 2.2: [[Quadratic Functions]]
**Section 2.3: [[Polynomial and Rational Functions]]
**Section 2.4: [[Exponential Functions]]
**Section 2.5: [[Logarithmic Functions]]
**Section 2.6: [[Applications:  Growth and Decay; Finance]]
**Section 3.1: [[Limits]]
**Section 3.2: [[Continuity]]
**Section 3.3: [[Rates of Change]]
**Section 3.4: [[Definition of the Derivative]]
**Section 3.5: [[Graphical Differentiation]]
**Section 4.1: [[Techniques for Finding Derivatives]]
**Section 4.2: [[Derivatives of Products and Quotients]]
**Section 4.3: [[The Chain Rule]]
**Section 4.4: [[Derivatives of Exponential Functions]]
**Section 4.5: [[Derivatives of Logarithmic Functions]]
**Section 5.1: [[Increasing and Decreasing Functions]]
**Section 5.2: [[Relative Extrema]]
**Section 5.3: [[Higher Derivatives and Concavity]]
**Section 5.4: [[Curve Sketching]]
**Section 6.1: [[Absolute Extrema]]
**Section 6.2: [[Applications of Extrema]]
**Section 6.3: [[Further Applications of Extrema]]
**Section 6.4: [[Implicit Differentiation]]
**Section 6.5: [[Related Rates]]
**Section 7.1: [[Antiderivatives]]
**Section 7.2: [[Substitution]]
**Section 7.3: [[Area and the Definite Integral]]
**Section 7.4: [[The Fundamental Theorem of Calculus]]
**Section 7.5: [[The Area Between Two Curves]]
**Section 7.6: [[Numerical Integration]]