Calculus Projects with Maple V

Formerly published as Calculus Laboratories with Maple, this book has been completely revised with a focus on developing students' problem-solving skills using calculus and fostering the spirit of open experimentation with the computer. Its laboratory-based investigations guide students through examples, then challenge them to solve a set of similar problems. Just as in chemistry and physics lab sessions, each Maple lab is started with a statement of the requisite machine commands, followed by a background section, which is tutorial in nature. The lab exercise ends with a statement of the minimal lab report required of the student. A collection of pedagogical notes is provided for the instructor in the Appendices to flag potential problems areas for students.

• Includes coverage of slopes of functions, graphs of polynomials, rational functions, Riemann sums, Taylor polynomials and convergence, and polar coordinates.

• Encourages students to spend their time on problem solving and conceptual understanding rather than on computation.

• Includes coverage of slopes of functions, graphs of polynomials, rational functions, Riemann sums, Taylor polynomials and convergence, and polar coordinates.

• Is fully compatible with Release 3 and Release 4.

• Added projects on Maple tutorial, third semester (multivariable) calculus, quadratic and cubic splines, curvature, integration of volumes, integration with Monte Carlo methods, and animations of involutes.

Table of Contents:

1. Slopes of Functions. 2. Graphs of Polynomial Functions. 3. Approximating Zeroes of Functions 4. Euler's Method and Skydiving. 5. A Simple Growth Model. 6. Rational Functions. 7. Applied Optimization: Otsego Electric Company. 8. Summations: Finite and Infinite. 9. Riemann Sums and Monotone Functions. 10. Definite Integrals and Computing Accuracy. 11. Remembrance of Things Past 12. Financial Mathematics 13. The Catenary: An Application. 14. Summations and Inductive Verification. 15. Difference Equations as Models of Differential Equations. 16. Taylor Polynomials and Convergence. 17. Lagrange Interpolation and Goodness of Fit. 18. Splines, I: Data Fitting. 19. Splines, II: Bezier Curves. 20. Koch's Fractal. 21. Polar Coordinates, I. 22. Polar Coordinates, II. 23. Parametric Conics. 24. Animated Cycloids and Planetary Gears. 25. Parametric Surfaces. 26. Exploring Cylindrical Coordinates. 27. Tangent Lines and Tangent Plants. 28. Constrained Optimization and Lagrange Multipliers. 29. Curvature. 30. Iterated Integrals. Appendices. Index.

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