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Review Review for Exam I Sample Exam - This was a previous midterm. Problems 2, 7 and 8 do not apply. Review for Exam II Practice Problems for Exam II Review for Final Exam Practice Problems for the Final - PDF Chapter 1 F=ma Main Characters Hipparchus of Rhodes 190-120 BC - seasonal inconsistencies Claudius Ptolemy 85-165 - epicycles and equants Nicolaus Copernicus 1473-1543 - heliocentric 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 - Sir Isaac Newton 1642-1727 - Law of Gravitation and Laws of Motion/Calculus Gottfried Wilhelm von Leibniz 1646-1716 - Calculus History Topics Orbits and gravitation Gravitation Planetary Motion Ptolemaic System - Applet Eccentric, epicycle and equant A Mathematical Supplement to “The Sun in the Church: Cathedrals ... Epicycloids and Hypocycloids Kepler's Laws - animation Ellipse Properties - Maple 8 File Motion on Parametric Curves Maple 8 Chapter 2 Vector Algebra Origins Sir William Rowan Hamilton (1805-1865) Quaternions Hermann Gunther Grassman (1809-1877) James Clerk Maxwell (1831-1879) Electricity and Magnetism Vector Calculus Course Vectors - Summary Lines, Planes and Vectors Lines.mws Maple 8 Worksheet Planes.mws Maple 8 Worksheet Chapter 3 Celestial Mechanics Plane and Space Curves PowerPoint Space Curve Gallery Watching Flies Fly Spirograph Frenet.mws - Plotting N, T, B for helix 2D Motion.mws - Section 1.6, Problem 5-10 Example 3D Motion.mws - Section 3.2 Problem 4-9 Example Hyperbolic Functions - MathWorld Proof that Diagonals of Parallelogram Bisect Problem 17 from Section 3.2 - Misguided Missle Problem (Maple 8 File) Chapter 4 Differential Forms Dr Lugo's notes on Differential forms from his Differential Geometry text Geometry and Physics: A Marriage Made in Heaven - Lecture by Sir Michael Atiyah - duration: 1:08:03, 23 slides and another video lecture at MSRI Geometry and Physics - From Plato to Hawking Introduction to differential forms, Introduction to differential forms II Differential Forms for Physicists Lecture on Differential Forms Differential forms and the polar planimeter Differential Forms Text in E&M A Short History of Geometry Chapter 5 Line Integrals and Multiple Integrals Introduction to Line Integrals Computing Line Integrals in Maple Riemann Sum Applet, Applet 2 Lebesgue Integral Multiple Integrals Notes on Multiple Integrals Multiple Integral Applications Integrals You Should Know! and Caculus at SOS Math Links for Integration Integration Practice Math 232 Spring 2003 Integration Techniques at Calculus@Internet Integration Using Your Rear View Mirror from Karl's Caculus Tutor - Look at all sections of the section on Methods of Integration! Integral Tables 1, 2, 3 Common Subsitutions and More, 4 Chapter 6 Linear Transformations Derivative as a linear map PlanetMath: derivative Practice Using Differentials Differentials; Linear and Quadratic ... Differentials; Linear and Quadratic Approximations Summary: ... Linear Transformations Linear Transformation -- from MathWorld Differential Form Computation in Maple 8 Determinants, Math World - Properties 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 Back in the saddle again .... Surfaces in Maple Plotting Some Surfaces The Torus and Tangent Planes More Maple Files for Surfaces Surf1.mws, trek.mws, klien.mws Web Applet for Drawing 3d Parametric Surfaces Parameterized Surfaces in Maple Chapter 8 Integration by Pullback Surface Area in Maple Surface Integrals Surfaces and surface integrals Homework Files Surface Area by Pullback Problem 8.6 #10 Surface Area of Torus Chapter 9 Techniques of Differential Calculus See FCM - Multivariate Calculus Pages! Implicit Function Theorem - Implicit differentiation, Math World, Planet Math, Some Problems Inverse Function Theorem - Special case of IFT! Taylor's Theorem Local Extrema - Maple File Lagrange Multipliers - Maple File Hessian Computation Weird Surfaces Triply Periodic Minimal Surfaces The Virtual Minimal Surface Museum A Minimal Surface Gallery A Surface Gallery Implicit Surfaces 1, 2, 3 Quadratic Surfaces Conic Sections - Diagonalization The General Quadratic, Quadratic Curve (MathWorld) Diagonalization of Quadratic Forms Examples of need for computing the Hessian Partial Hessian Vibrational Analysis ... Normal Mode Analysis without the Hessian Chapter 10 The Fundamental Theorem of Calculus Calc III Final Green's Theorem, Divergence Theorem, Stoke's Theorem Examples, and more: Stoke's Theorem, Divergence Theorem, Green's Theorem Chapter 11 E=mc² Read Over Winter Break! Top

E-Mail: Dr. Russell Herman		Last Updated: November 29, 2005

Materials