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Animating Calculus is the result of an inspired collaboration between Ed Packel, who is experienced in the integration of computers and mathematics in the classroom, and Stan Wagon, well-known mathematical expositor and author of the acclaimed Mathematica in Action (1991, WH Freeman). It contains 22 laboratory notebooks that use Mathematica. With its superior animations and graphics, and coverage ranging from standard topics to new and unusual extensions and applications, Animating Calculus is a remarkable tool for experiencing and learning about calculus on the computer. Animating Calculus includes: Demonstrating and interactive exercises emphasizing mainstream calculus but including ancillary topics and applications. Focus on important, fundamental ideas and applications rather than the everyday mechanics of a computer algebra system. Sophisticated computer animations that clarify geometric concepts in calculus. Discussions of numerical and graphical pitfalls that stress the importance of verifying results.
LAB 1 Initiation.- LAB 2 Plotting.- LAB 3 Derivatives: Measuring the Rate of Change.- LAB 4 The Race to Infinity.- LAB 5 Indeterminate Limits and L’Hôpital’s Rule.- LAB 6 Using Calculus to Land an Airplane.- LAB 7 Max-Min Methods: Mind Meets Machine.- LAB 8 Staying on Track with Newton’s Method.- LAB 9 Population Dynamics, Iteration, and Chaos.- LAB 10 What Is an Integral?.- LAB 11 The Fundamental Theorem.- LAB 12 The Needle Problem.- LAB 13 Integration by Machine.- LAB 14 Numerical Integration.- LAB 15 Differential Equations and Euler’s Method.- LAB 16 Probability and Calculus.- LAB 17 Roses, Snails, and Butterflies.- LAB IS Rolling Wheels.- LAB 19 Infinite Series of Constants.- LAB 20 Rhythm and Dissonance in the Harmonic Series.- LAB 21 Polynomial Approximation and Taylor Series.- LAB 22 A Deceptive Definite Integral.- APPENDIX 1 Troubleshooting.