Mathematics 365 :: Complex Variables :: Spring 2007

Instructor: Michael Bolt, 292 North Hall, x6-6719, mbolt@calvin.edu.

This course is an introduction to the theory and application of functions of one complex variable. Applications include using harmonic functions to solve for the distribution of a steady-state temperature or electrostatic charge, and to solve for non-viscous fluid flow. A working knowledge of complex analysis can be an important part of the education of any scientist or engineer.

Topics include: Complex numbers, complex functions, integration and the Cauchy integral formula, power series, residues and poles, and conformal mapping. Prerequisite: Mathematics 261 or 232.
Important Dates
There will be three in-class tests on the following days:
The final exam will be Wednesday, May 16, 9am--12pm.
Homework and Tests
P. Set 01 due Friday, Feb 02: [pdf] : [soln]
P. Set 02 due Friday, Feb 09: [pdf] : [soln?]
P. Set 03 due Friday, Feb 16: [pdf] : [soln?]
P. Set 04 due Friday, Feb 23: [pdf] : [soln?]
P. Set 05 due Monday, Mar 05: [pdf] : [soln]
P. Set 06 due Friday, Mar 09: [pdf] : [soln]
P. Set 07 due Monday, Mar 16: [pdf] : [soln]
P. Set 08 due Tuesday, Apr 03: [pdf] : [soln]
P. Set 09 due Friday, Apr 13: [pdf] : [soln]
P. Set 10 due Friday, Apr 20: [pdf] : [soln]
P. Set 11 due Friday, Apr 27: [pdf] : [soln]
P. Set 12 due Wednesday, May 2: [pdf] : [soln]
P. Set 13 due Friday, May 11: [pdf] : [soln]

In-class Handouts & Demonstrations

[Jan 31] : Domain Coloring : the color map and three 4th degree polynomials
[Feb 2] : Domain Coloring (more)
[Feb 2] : Mathematica package for domain coloring: http://www.kfunigraz.ac.at/imawww/vqm/pages/dlgraph.html
[Feb 5] : Domain Coloring : Arg z and |z|
[Feb 6] : Complex function viewer at Texas Tech: Viewer
[Feb 6] : Complex function viewer at Santa Cruz: Bombelli
[Feb 9] : Domain Coloring : Limits and Continuity
[Feb 13] : Domain Coloring : CR equations
[Feb 19] : Domain Coloring : Iterating Newton's method
[Feb 19] : Martin Pergler's page on Domain Coloring
[Feb 20] : Domain Coloring : Convergence of power series
[Feb 21] : Exponential Function : Mathematica notebook to accompany Mathews & Howell
[Feb 21] : Domain Coloring : Exponential function and convergence of its partial sums
[Feb 21] : Domain Coloring : By Hans Lundmark; see Figure 4 for the color scheme
[Feb 21] : Domain Coloring : By Hans Lundmark; Taylor polynomials of the exponential function
[Mar 09] : Domain Coloring : Example for Cauchy-Goursat and Deformation of Contour
[Mar 30] : Domain Coloring : Example of Laurent series
[Apr 02] : Domain Coloring : Singularities
[Apr 11] : Domain Coloring : Improper integrals
[Apr 13] : Domain Coloring : Improper integrals
[Apr 16] : Domain Coloring : Improper integrals

You can view notebook (.nb) files using the free program MathReader, available at http://www.wolfram.com/products/mathreader/.

Additional Links