Materials


	Course Materials
			Back
Chapter 1 F=ma Main Characters Hipparchus of Rhodes 190-120 BC - seasonal inconsistencies Claudius Ptolemy 85-165 - Eccentric, epicycle and equant Nicolaus Copernicus 1473-1543 - heliocentric vs geocentric Tycho Brahe 1546-1601 - planetary data Galileo Galilei 1564-1642 - scientific method - study of kinematics Johannes Kepler 1571-1630 - Planetary Laws Isaac Barrow 1630-1677 - Newton's Teacher - Genealogy Tree Sir Isaac Newton 1642-1727 - Law of Gravitation and Laws of Motion/Calculus Gottfried Wilhelm von Leibniz 1646-1716 - Calculus Edmond Halley 1656-1742 History of Calculus History of Notation Florian Cajori paper Leibniz-Newton Controversy Timeline of Calculus History History Topics Orbits and gravitation Gravitation The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time Planetary Motion A Mathematical Supplement to “The Sun in the Church: Cathedrals ... Epicycloids and Hypocycloids Planetary Law Simulator Kepler's Laws - animation Newton's proof of Kepler's second law Philosophić Naturalis Principia Mathematica - Newton Proposition I Proposition II Proposition XI Ellipse Properties - Maple 8 File Motion on Parametric Curves Maple 8 Chapter 2 Vector Algebra Max Tegmark's Mathematics Learning Map - Depiction of mathematics field relations Origins M.J. Crowe speaks at U. Louisville, 2002 - A History of Vector Analysis Sir William Rowan Hamilton (1805-1865) Quaternions Hermann Gunther Grassman (1809-1877) Peter Guthrie Tait (1831-1901) - Nabla James Clerk Maxwell (1831-1879) Electricity and Magnetism William Kingdon Clifford (1845-1979) Separation of Grassman product Josiah Willard Gibbs (1839 - 1903) Oliver Heaviside (1850-1925) Multivariable Calculus Videos MIT Opencourseware Videos at Berkeley Donny Lee's YouTube Videos Calc III - Dr. Herman's Course Vectors - Summary Lines, Planes and Vectors Lines.mws Maple 8 Worksheet Planes.mws Maple 8 Worksheet Scalar Equation of Plane - YouTube Video Pauls' Online Notes Dot Product Cross Product Cross Product Calculator Diagonals of parallelogram bisect Chapter 3 Celestial Mechanics National Curve Bank Fifty Famous Curves PDF Space Curve Gallery Watching Flies Fly Spirograph Frenet.mws - Plotting T, N, B for helix TNB Plots Frenet Frame Example Oscullating Circles: 2D Curves, Helix, Elliptical Helix, Tornado, Twisted Cubic Osculating Circles for several curves A Shortcut to Finding The Unit Normal and Binormal Vectors Hyperbolic Functions - MathWorld Maple Files Curvature and Osculating Plane - Maple 10 2D Motion.mws 3D Motion.mws Misguided Missle Chapter 4 Differential Forms The history of differential forms from Clairaut to Poincaré - Victor J. Katz Differential Forms, the Early Days; - Han Samelson Geometry and Physics - From Plato to Hawking Lecture by Sir Michael Atiyah Introduction to differential forms, Introduction to differential forms II Differential Forms for Physicists Lecture on Differential Forms Dr Lugo's notes on Differential forms from his Differential Geometry text Differential forms and the polar planimeter Using differential forms in E&M Computing Products of Forms - Maple File Chapter 5 Line Integrals and Multiple Integrals Line Integrals - Paul's Online Math Notes Computing Line Integrals in Maple Multiple Integrals - Paul's Online Math Notes Multiple Integrals Double Integral Examples Iterated Integrals and Area Double Integrals and Volumes Integrals You Should Know! and Caculus at SOS Math Integration Practice Math 232 Spring 2003 IIntegral Tables Common Integrals, Common Subsitutions and More Dave's Math Tables The Integrator integrate (integrate x^2 y^2 from 0 to y) y from 0 to 1 at Wolframalpha.com Thin Plate Problem Chapter 6 Linear Transformations Derivative as a linear transformation Practice Using Differentials Differentials; Linear and Quadratic ... Linear Map - Wikipedia Linear Transformation -- from MathWorld Apply 2x2 Transformation to a photo Differential Form Computation in Maple 8 Math World - Determinant Properties Iterated Function Systems Determinants Handout Project files - Instructions, MoveTri.m, Chapter 7 Differential Calculus Maple Demos: Directional Derivative, Partial Derivative, Contour Plots - Maple File Level Curves and Surfaces in Maple Gradient and Contours - Maple File The Chain Rule Surfaces in Maple Plotting Some Surfaces - Simple Maple Worksheet The Torus and Tangent Planes - Maple Worksheet, more advanced More Maple Files for Surfaces trek.mws, klein.mws Web Applet for Drawing 3d Parametric Surfaces Parametric Curves and Surfaces in Maple Parametric surfaces in MATLAB Chapter 8 Integration by Pullback Surface Integrals Parametrized Surfaces and Surface Integrals - Examples Weird Surfaces Triply Periodic Minimal Surfaces The Virtual Minimal Surface Museum A Minimal Surface Gallery A Surface Gallery Implicit Surfaces Banchoff's Mathematical Artwork Student's homework - Can you get Maple to do this? From Cassidy Curtis Videos Surface Integrals with Parameterized Surface - Part 1 Other Videos Maple Files Surface Area in Maple - (surf2.mws) Surface Area by Pullback Problem 8.6 #10 or here Surface Area of Torus Chapter 9 Techniques of Differential Calculus Implicit Function Theorem - Math World, Planet Math Economic Application of Implicit Differentiation Local Extrema - Maple File Lagrange Multipliers - Maple File Hessian Computation Maple File Conic Sections - Diagonalization The General Quadratic, Quadratic Curve (MathWorld) Diagonalization of Quadratic Forms Examples of using the Hessian Partial Hessian Vibrational Analysis ... Normal Mode Analysis without the Hessian Examples of using Lagrange Multipliers Paul's Notes Extremizing the volume of a box - Fixed surface area and edge length Rectangular box without a lid Practice Problems YouTube Videos, and Video for Two Constraint Problem Homework - tent.mws, trough.mws, two constraints Chapter 10 The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus Handout or PDF Differential Forms and Integration by Terence Tao, a leading mathematician of this decade Green's Theorem, Divergence Theorem, Stokes' Theorem Examples, and more: Stokes' Theorem, Divergence Theorem, Green's Theorem Dr. Herman's Notes/Problems - Vector Analysis Vector Calculus Identities The Mathematical Papers of the Late George Green Planimeter - Application of Green's Theorem YouTube Green's Thm Example Stokes'/Divergence Thm Examples Surface Integrals - Can you keep up? See MIT Recitations for examples - Use Green's Thm to get area Verify Stokes' Thm Lagrange Multiplier or MIT lectures - Stokes' Thm Maxwell's Equations Watch Video - Mathematics Gives You Wings Differential Forms and Stokes' Theorem by Jerrold E. Marsden The Poincare' Lemma and de Rham Cohomology The Fundamental Theorem and Poincare's Lemma Chapter 11 E=mc² Read Over Winter Break! Reviews Review for Exam I (MS Word) Sample Exam (MS Word) Pg1, Pg2 Review for Exam II (MS Word) Sample Exam (MS Word) Pg1, Pg2 Review for Final (PDF) Sample Final (PDF) Extra Problems (MS Word) Top

E-Mail: Dr. Russell Herman		Last Updated: August 18, 2016

Materials