Problems are from the assigned textbook: E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis with Applications to Engineering and Science, 3rd Edition, Prentice-Hall, 2003.
The following is a minimal set of problems you should be able to solve by the end of the course. Additional practice, while highly recommended, is up to your discretion.
| Date | Topic | Problems |
|---|---|---|
| Sep 11 | algebra of complex numbers | §1.1; #7, 9, 15, 16, 20, 23, 24 |
| complex plane | §1.2; #7, 9, 13, 15, 16 | |
| polar form | §1.3; #4, 7 | |
| complex exponential | §1.4; #1, 3, 8 | |
| Sep 21 | quiz #1 | |
| Sep 21 | complex exponential | §1.4; #11, 12, 13, 23 |
| powers and roots | §1.5; #4, 5, 6, 7 | |
| complex functions | §2.1; #1ac, 4, 13ab | |
| Sep 28 | quiz #2 | |
| Sep 28 | limits | §2.2; #11cd(note typo), 25bc |
| derivatives | §2.3; #4, 9 | |
| Cauchy-Riemann equations | §2.4; #1, 3, 5, 8 | |
| Oct 5 | quiz #3 | |
| Oct 5 | Polynomials & Rational Functions | §3.1; #1, 3, 4, 6, 13, 15ab |
| Transcendental functions | §3.2; #5acd, 10, 17 | |
| Oct 12 | quiz #4 | |
| Oct 12 | Logarithms | §3.3; #1, 3, 5 |
| Contour integrals | §4.2; #5, 6, 8 | |
| Oct 26 | midterm exam #1 | |
| Oct 26 | Integral theorems | §4.4; #10, 13, 15, 16, 17 |
| Residue theorem | §6.1; #1, 3abc | |
| Nov 4 | quiz #5 | |
| Nov 4 | Integrals on the real line | §6.3; #1, 3, 5, 9, 11 |
| Trigonometric integrals | §6.2; #2, 3, 5, 8 | |
| More integrals | §6.4; #1, 3, 5, 8 | |
| Nov 16 | quiz #6 | |
| Nov 16 | Indented contours | §6.5; #2, 3, 5, 9 |
| Series | §5.1; #1ab, 2ac, 11ac | |
| Taylor series | §5.2; #1abe | |
| Nov 16 | quiz #7 | |
| Nov 23 | midterm exam #2 | |
| Nov 23 | Laurent series | §5.5; #1, 3, 7, 9 |
| Dec 7 | final lecture | |
| Dec 14 | final exam - 09:00 OM 2771 |
December 4, 2015