Getting Started

Getting Started Editing Formulas Variables, Expressions, and Functions Vectors Graphs Programming Control Key Map Samples

Starting a Formula Navigating in a Formula Arithmetic Operations Subscripts, Superscripts, Under and Over Parentheses and Absolute Value Writing Applet Tags Starting a Formula Click the mouse in an open area to start a new formula. A small box with a blinking text cursor will appear. As you type, text will appear in the box. You may insert a symbol by right clicking (control click on a Mac) and selecting Symbols from the popup menu. Symbols may also be inserted with Control <ctrl> characters. See Control Key Map for a list of control key shortcuts. Navigating in a Formula When a formula has keyboard focus, there will be a box around a portion of the formula, and a blinking text cursor will appear in the box. To give a formula focus, click the mouse inside the formula. Each formula has the structure of a "binary tree". Example: The formula 5 + 3 + 4 has the following tree structure Here is that formula in the applet: Click in the formula above to select it. If the box does not contain the entire formula, then press the "up arrow" key until the entire formula is boxed. You have now shifted the focus to the head node of the formula, the first plus. At this point the left arrow key will select the 5. When the 5 is selected, the up arrow will select the head node, the first plus. When the head node is selected, the right arrow will select the second plus. Arithmetic Operations The arithmetic operations correspond to the following characters: Addition: + Subtraction: - Multiplication: * Division: / Power: ^ Factorial: ! Summation: <ctrl>s Summation requires the "Under/Over" structure. An example is given in the next section on Subscripts, Superscripts, Under and Over. Example: the calculation 5 + 4 - 3 = 6 is done with the key strokes 5 + 4 - 3 <ctrl> z Control z is used to evaluate expressions. Try it. Click the mouse below the following formula to start a new formula, then use the key strokes indicated above. Example: the key strokes 4 + 5 / 2 - 7 / 8 <ctrl> z produce the following formula. Try it by clicking below the formula and using the key strokes. In the previous example, the fraction 7/8 was subtracted from 2. Suppose that you want to compute (5/2)-(7/8), where 7/8 is subtracted from the fraction 5/2. After typing 5/2, you must use the up arrow to shift the focus to the fraction. Here are the key strokes: 5 / 2 <up arrow> - 7 / 8 <ctrl> z Example: The key strokes to calculate 23+3=11 are 2 ^ 3 <up arrow> + 3 <ctrl> z Subscripts, Superscripts, Under and Over Subscript: <ctrl> j Superscript: ^ Sub and Superscript: <ctrl> k Under: <ctrl> u Over: <ctrl> o Under and Over: <ctrl> i The applet below shows these six structures. Example: Summation The sum 1 + 3 + 5 + 7 + 9 can be written in Sigma-notation as follows. The key strokes to generate this formula are: <ctrl> s <ctrl> i 4 <right arrow> i = 0 <up arrow> <up arrow> ( 2 * i + 1 <ctrl> z Note that after typing i = 0, one up arrow shifts the focus to the equality, and another up arrow is required to shift focus to the summation structure. Also note that typing the open parenthesis ( creates the group consisting of both an open and a close, so it is not necessary to type the close parenthesis ). Parentheses and Absolute Value Typing an open parenthesis ( creates a set of parentheses, so it is not necessary to type the close parenthesis ). An existing node may be enclosed in parentheses by selecting it and typing <ctrl> 9. A set of absolute value bars is created when you type |. An existing node may be enclosed in absolute value bars by selecting it and typing <ctrl> 0 (zero). Example: 3 + 4 - 9 = -2 Starting with 3 + 4 - 9, you would enclose the 4 - 9 in absolute value bars by selecting the - node, then typing <ctrl> 0. The result would be 3 + |4 - 9|, which evaluates to 8. Writing Applet Tags This feature is for creating web pages that contain copies of the applet. Clicking the Edit button and selecting write presents two options, an Inline Tag or a Full Tag. Selecting one of these options opens a text box containing the appropriate APPLET tag that may be copied to the clipboard and pasted into an HTML document. The directory containing the HTML file needs to contain the JAR file jme.jar. The Inline Tag produces a copy of the applet with no border. The size of the applet is adjusted so that all the formulas and graphs that were present when the tag was written will appear. All of the copies of the applet that have appeared so far on this page have been in Inline form. An example of the applet in Full form appears below. The Full Tag produces a copy of the applet with its border, scrollpane, message window, Settings and Edit buttons. The applet will contain all the formulas and graphs that were present when the tag was written. The applet will be 600 pixels wide and 400 pixels high. Here is the Full form of the applet. Click Edit and select write to see the tags.