Math 317: Complex Analysis

Fall 2025

Department of Mathematics and Statistics, Grinnell College

Class # Date Reading Brief description Assignment
1 F Aug 29 I.1 - I.3 Complex numbers and their representations -
- M Sep 1 - No class - labor day -
2 W Sep 3 I.4 - I.5 Elementary functions I Quiz 1
3 F Sep 5 I.6 - I.8 Elementary functions II -
4 M Sep 8 II.1 Topology of the plane HW 1
5 W Sep 10 II.2 Analytic functions Quiz 2
6 F Sep 12 II.3 The Cauchy-Riemann equations -
7 M Sep 15 II.4 Inverse mappings HW 2
8 W Sep 17 II.5 Harmonic functions Quiz 3
9 F Sep 19 II.6 Conformal mappings -
10 M Sep 22 II.7 Linear fractional transformations HW 3
11 W Sep 24 III.1 Line integrals Quiz 4
12 F Sep 26 III.2 Independence of path of integration -
13 M Sep 29 III.3 Harmonic conjugates HW 4
14 W Oct 1 III.4-III.5 Mean value property and the max. modulus principle Quiz 5
15 F Oct 3 III.6 Application to fluid dynamics -
16 M Oct 6 IV.1 Complex line integrals HW 5
17 W Oct 8 IV.2 Fundamental theorem of calculus for analytic functions Quiz 6
18 F Oct 10 IV.3 Cauchy's Theorem -
19 M Oct 13 IV.4 Cauchy's integral formula HW 6
20 W Oct 15 - Q & A -
21 F Oct 17 - Midterm exam Exam
- Oct 20 - 24 - No class - fall break -
22 M Oct 27 IV.5 Liouville's Theorem -
23 W Oct 29 IV.6 Morera's Theorem -
24 F Oct 31 IV.7 Consequences of Morera -
25 M Nov 3 V.1 Series HW 7
26 W Nov 5 V.2 Sequences of functions Quiz 7
27 F Nov 7 V.3 Power series -
28 M Nov 10 V.4 Power series expansion of an analytic function HW 8
29 W Nov 12 V.5 Power series expansion at inifnity Quiz 8
30 F Nov 14 V.6 Manipulation of power series -
31 M Nov 17 V.7 Zeros of an analytic function HW 9
32 W Nov 19 VI.1 The Laurent decomposition Quiz 9
33 F Nov 21 VI.2 Isolated singularities of analytic functions -
34 M Nov 24 VI.3 Isolated singularities at infinity HW 10
35 W Nov 26 VI.4 Partial fraction decomposition Quiz 10
- Nov 27 - 31 - no class - Thanksgiving break -
36 M Dec 1 VII.1 The Residue Theorem -
37 W Dec 3 VII.2 Real integrals with complex methods I -
38 F Dec 5 VII.3 Real integrals with complex methods II -
39 M Dec 8 VII.4-VII.5 Real integrals with complex methods III HW 11
40 W Dec 10 VII.6 Principal values Quiz 11
41 F Dec 12 - Wrap up -
42 Th Dec 18 - Final Exam Exam

“The best thing for being sad," replied Merlin, beginning to puff and blow, "is to learn something. That's the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then — to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting. Learning is the only thing for you. Look what a lot of things there are to learn.”

― T.H. White, The Once and Future King