Math 13, Fall 2004
Calculus of Vector-Valued Functions
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.