Time and Location: | Tue, Thur 12:30 - 1:45 pm, DSH-328 |
Office Hours: | Tue, Thur, 11 - 11:50 am in SMLC 212 and also by appointment in Zoom |
Professor Info: | Anna Skripka, skripka [at] math [dot] unm [dot] edu |
Week |
Class dates |
Book sections |
Topics |
1 |
Aug 22, 24 |
1.1, 1.2, 1.3; Schaum p. 9-32 |
Complex numbers. Polar form. |
2 |
Aug 29, 31 |
1.4, 1.5; home reading: 1.6 |
Complex exponential. Roots. Planar sets. |
3 |
Sep 5, 7 Drop with no grade: Sep 10 |
2.1, 2.2; Schaum p. 62-67 |
Functions of complex variables. Limits and continuity. |
4 |
Sep 12, 14 |
2.3, 2.4, 2.5; Schaum p. 85-96 |
Analytic functions. Cauchy-Riemann equations. Harmonic functions. |
5 |
Sep 19, 21 |
3.1, 3.2, 3.3 |
Polynomials and rational functions. Exponential, trigonometric, and logarithmic functions. |
6 |
Sep 26, 28 |
3.4, 3.5 |
Application: boundary value problems. Complex powers & inverse trigonometric functions. |
7 |
Oct 3, 5 (Exam 1) |
covered material of 1.1-3.3 |
Review. |
8 |
Oct 10 |
4.1, 4.2, 4.3 |
Complex integration. |
9 |
Oct 17, 19 |
4.4, 4.5, 4.6; home reading: 5.1; Schaum p. 184-186 |
Cauchy's integral theorem. Cauchy's integral formula. Bounds for analytic functions. |
10 |
Oct 24, 26 |
5.2, 5.3, 5.5; Schaum p. 188-190 |
Review of series. Power, Taylor, and Laurent Series. | 11 |
Oct 31, Nov 2 |
5.6, 5.7, 6.7 |
Classification of singularities. Argument principle and Rouche's theorem. Uniqueness. | 12 |
Nov 7, 9 Withdrawal deadline: Nov 10 |
6.1, 6.2, 6.3, 6.4; Schaum p. 214-226 |
Residue theorem and its applications. Trigonometric integrals. Improper integrals. |
13 |
Nov 14, 16 (Exam 2) |
3.4,3.5,4.1-4.6,5.1-5.7,6.7 |
Review. |
14 |
Nov 21 |
6.5, 6.6 |
Indented contours. Integrals involving multiple-valued functions. |
15 |
Nov 28, 30 |
7.1, 7.2, 7.3 |
Conformal mappings and their applications. Möbius transformations and boundary value problems. |
16 |
Dec 5, 7 |
7.4, 7.6 |
Boundary value problems. Review. |
17 |
Dec 14 (Thursday),
10 am - noon
Final Exam |