Multivariable Calculus and Mathematica®

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 1-15

3. Vectors and Graphics

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 17-34

4. Geometry of Curves

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 35-63

5. Kinematics

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 65-80

6. Directional Derivatives

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 81-102

7. Geometry of Surfaces

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 103-131

8. Optimization in Several Variables

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 133-151

9. Multiple Integrals

   • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

   Pages 153-183

10. Physical Applications of Vector Calculus

    • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

    Pages 185-209

11. Mathematica Tips

    • Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

    Pages 211-224

12. Back Matter

    Pages 225-283

    PDF

One of the authors' stated goals for this publication is to "modernize" the course through the integration of Mathematica. Besides introducing students to the multivariable uses of Mathematica, and instructing them on how to use it as a tool in simplifying calculations, they also present intoductions to geometry, mathematical physics, and kinematics, topics of particular interest to engineering and physical science students. In using Mathematica as a tool, the authors take pains not to use it simply to define things as a whole bunch of new "gadgets" streamlined to the taste of the authors, but rather they exploit the tremendous resources built into the program. They also make it clear that Mathematica is not algorithms. At the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The problem sets give students an opportunity to practice their newly learned skills, covering simple calculations with Mathematica, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numberical integration. They also cover the practice of incorporating text and headings into a Mathematica notebook. A DOS-formatted diskette accompanies the printed work, containing both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students. This supplementary work can be used with any standard multivariable calculus textbook. It is assumed that in most cases students will also have access to an introductory primer for Mathematica.

• Clean
• Mathematica
• Numerical integration
• algorithm
• algorithms
• automation
• electricity
• kinematics
• mathematical physics
• mathematical software
• optimization

• Department of Mathematics, University of Maryland, College Park, USA

  Kevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

Policies and ethics