Title: Animating calculus : Mathematica notebooks for the laboratory /
Authors: Packel, Edward W.; Wagon, S.
Publisher: TELOS,
Year: 1996
Subjects: Mathematica (Computer file); Calculus Computer-assisted instruction.
Abstract: Animating Calculus is designed to help you explore calculus and visualize concepts through the use of computation and animation. This collection of 22 labs, together with the computer algebra system Mathematica, can be used for self-study, demonstration, or as a laboratory supplement to an existing calculus sequence. Standard calculus topics as well as new and unusual extensions and applications are presented, including derivatives and rate of change, calculus and landing airplanes, population dynamics and iteration, the fundamental theorem, The Buffon needle problem, numerical and symbolic integration, rolling wheels (round and square), subtleties of the harmonic series, and more.
Contents: 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'Hopital'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 18. 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 Definitive Integral -- App. 1. Troubleshooting -- App. 2. Usage Messages for Animating Calculus Objects.