Math 13, Fall 2004

Calculus of Vector-Valued Functions

General Information Syllabus Homework Assignments Exam Related Class Material

Handouts used in the class

What is Maple?

Maple is a computer program for doing a variety of symbolic, numeric, and graphical computations. Such a program is commonly called a CAS, short for Computer Algebra System. Maple also provides a programming environment, with a syntax similar to that of pascal. In fact, most of the Maple commands are written in the Maple programming language. It is possible to look at the source for most of the Maple commands, and experience programmers can add their own modifications and extensions to Maple.

Maple was originally developed as a joint research project centered at the University of Waterloo and ETH Zurich. It is now marketed by MapleSoft.

What kind of problems can Maple solve?

Maple performs best on problems involving symbolic, as opposed to numerical computation. However, it is generally easier to use Maple on numerical problems rather than write programs in FORTRAN or C, for numerical calculations that are not too involved. Maple also provides the user with a lot of graphical power.

Where one can find tutorials and guides for Maple?

Extensive Learning Guide and Getting Started Guide can be downloaded from MapleSoft. Tutorials and examples are available from Maple Application Center.

How can Maple be used at Dartmouth?

All enrolled Dartmouth students can download the latest version of Maple for free from Dartmouth Software Resources web page.

Introduction: Basic information about the course.

1.4 Vector Products: Summary of Products Involving Vectors.

1.7 Coordinate Systems: full page, pocket size for the plane coordinate systems, and pocket size for the space coordinate systems handouts.

2.2 Limits and Derivatives: Major facts about limits, continuity, and derivatives.

2.3 Derivatives: Major facts about derivatives as a pocket-sized handout.

2.3 Differentiability: Non-differentiable function that has both its partial derivatives. Maple demo in Maple Worksheet, PDF, and HTML format and a handout.

2.4 Mixed partial derivatives: Function that has different mixed partial derivatives. Maple demo in Maple Worksheet, PDF, and HTML format and a handout.

2.5 The chain rule: Example of the multi-dimensional chain rule.

2.6 Directional Derivatives: full page and pocket size handouts.

3.4 Gradient, Divergence, and Curl: Basic Identities of Vector Analysis.

5.2 Double Integral: Major facts.

5.5 Change of Variables: Summary.

5.6 Applications of Integration: Formulas for computing average values and center of mass.

6.2 Green's Theorem: full page and pocket size handouts.

7.1 Parametrized Surfaces: Maple demo in Maple Worksheet, PDF, and HTML format.

7.2 Surface Integrals: handout.

7.3 Stokes's and Gauss's Theorems: handout.