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Principal source for the topics below is the text by Mathews and Howell. Not everything of importance will be covered in lecture: you will need to learn some things from reading textbook assignments, doing Mathematica work, and solving homework sets.
How far we progress in the topics list depends on the pace we maintain.
- Complex numbers: their algebra, geometry, and topology [Chap. 1]
- Complex functions [Chap. 2]
- Analytic and harmonic functions [Chap. 3]
- Complex sequences, series, and power series [Chap. 4]
- Elementary functions (exponential, log, trig) [Chap. 5]
- Some applications of harmonic functions [selection from Chap. 10]
- Contour integrals [Chap. 6]
- Taylor and Laurent series [Chap. 7]
- Residues [Chap. 8]
- Conformal mapping [selection from Chap. 9]
See also the Aims page for a list of the overall aims of the course.
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