Maple via Calculus

1. Front Matter

   Pages i-xiii

   PDF

2. Basic Plotting

   • Robert J. Lopez

   Pages 1-6

3. Parametric Equations

   • Robert J. Lopez

   Pages 7-14

4. Optimization Problems

   • Robert J. Lopez

   Pages 15-18

5. Interpolation

   • Robert J. Lopez

   Pages 19-22

6. Conic Through Five Points

   • Robert J. Lopez

   Pages 23-25

7. An Implicit Function

   • Robert J. Lopez

   Pages 26-29

8. Inverse Functions

   • Robert J. Lopez

   Pages 30-33

9. Partial Fraction Decomposition

   • Robert J. Lopez

   Pages 34-37

10. Derivatives By Definition

    • Robert J. Lopez

    Pages 38-42

11. Implicit Differentiation

    • Robert J. Lopez

    Pages 43-43

12. Taylor Polynomials

    • Robert J. Lopez

    Pages 44-48

13. Teaching the Definite Integral

    • Robert J. Lopez

    Pages 49-54

14. Deriving Simpson’s Rule

    • Robert J. Lopez

    Pages 55-56

15. Numerical Integration

    • Robert J. Lopez

    Pages 57-61

16. Improper Integrals

    • Robert J. Lopez

    Pages 62-67

17. Integration by Trigonometric Substitution

    • Robert J. Lopez

    Pages 68-70

18. Integration by Parts

    • Robert J. Lopez

    Pages 71-72

19. Integration by Parts Twice

    • Robert J. Lopez

    Pages 73-75

20. Surface Area of a Solid of Revolution

    • Robert J. Lopez

    Pages 76-79

Modern software tools like Maple have the potential to alter radically the way mathematics is taught, learned, and done. Bringing such tools into the classroom during lectures, assignments, and examinations means that new ways oflooking at mathematics can becomepermanent fixtures ofthe curriculum. It is universal access that will make a software-based approach to mathematics become the norm. In 1988, with NSF funding under an III grant, I had the opportunity to bring Maple into the calculus classroom at Rose-Hulman Institute of Technology. Since then a new curriculum based on the availability ofcomputer algebra systems has evolved at RHIT and in my own courses. This volume contains a record of some of the insights gained into pedagogy using Maple in calculus. The activities and ideas captured in these Maple worksheets reflect concepts in calculus imple­ mented in Maple. There is an overt message to the reader that carries with it a side effect. However, it is possible that for one reader the side effect is the message and the message is the side effect! I had intended to put before my audience examples extracted from my Maple based curriculum to entice a wider acceptance ofthe benefits of making a computer algebra system become the basis of a revised calculus syllabus. By examples I had hoped to demonstrate the "rightness" of using software tools for teaching and learning calculus.

• Finite
• Interpolation
• Maple
• algebra
• calculus
• computer algebra system
• equation
• function
• mathematics

• Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, USA

  Robert J. Lopez

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