In the first half of the course we will study the calculus of differentiable complex-valued functions of a complex variable. This week we will begin by reviewing properties of the complex numbers themselves and studying the geometry/topology of the complex plane. On Friday, we will be in the lab learning the basics of Maple and seeing what options we have for graphical representations of complex-valued functions of a complex variable. (Since the graph of such a function is a four-dimensional object, we cannot represent it directly on a two-dimensional computer screen.)

Lab Activity for Friday, January 15

We will work in teams of two or three in Rooms 032Physics. The instructions for this activity can be found on the web at the Connected Curriculum Project

Parts 1-10 of this module describe the basic workings of Maple and the applications to calculations in calculus. Parts 11 and 12 deal with capabilities for representing and solving ordinary differential equations. We will not need this right away, and these parts can be skipped. Parts 13 and 14 deal with complex numbers and complex functions respectively. The Appendix describes the use of palettes -- a feature available in Release 5, but not Release 4.

The main emphasis in this lab activity is on learning and/or reviewing Maple. There will be a short report -- answering the questions posed in Part 14. Instructions on how to do this will be given out on Wednesday.

• If you have no experience with Maple, work through Parts 1-10, 13, 14, and the Appendix.

• If you are familiar with Release 4 but not Release 5, look over Parts 1 and 10 and the Appendix. Then work through Parts 13 and 14.

• If you are familiar with Release 5, work through Parts 13 and 14.

Assignment for Wednesday, January 20

Read Section 17.1 in the text.
Write out and turn in solutions to the following exercises in Section 17.1:

• 1, 3, 5, 6, 7,
• 14, 23, 24, 26
• 30 (Note that the right-hand side is printed incorrectly. It should be 2|z|² + 2|w|²)

Last modified: January 8, 1999