| Lec. | Date | Chapter | Topic |
|---|---|---|---|
| 1 | 8/24 | 1 | Complex numbers and operations. |
| 2 | 8/26 | 1 | Roots of unity, conjugation, modulus, inequalities. |
| 3 | 8/28 | 2 | Complex-valued functions; regions in the complex plane. |
| 4 | 8/31 | 2 | Circles and lines; the Riemann sphere. |
| 5 | 9/2 | 2 | Möbius transformations and circlines. |
| 6 | 9/4 | 3 | Open and closed sets in the complex plane. |
| - | 9/7 | - | Labor Day - No Classes |
| 7 | 9/9 | 3 | Limit points, closure, bounded sets, compact sets. |
| 8 | 9/11 | 3 | Convexity, connectedness, polygonal connectedness. |
| 9 | 9/14 | 3 | Sequences of complex numbers. |
| 10 | 9/16 | 3 | Sequences. Limits of functions and continuity. |
| 11 | 9/18 | 3, 4 | Continuous functions on compact sets. Curves. |
| 12 | 9/21 | 4 | Paths and contours. |
| 13 | 9/23 | 5 | Differentiability and Cauchy-Reimann equations. |
| 14 | 9/25 | 5 | Holomorphic functions. |
| 15 | 9/28 | 5 | Holomorphic functions. Zeros of functions. |
| 16 | 9/30 | Problems from Chapters 1-4 | |
| 17 | 10/2 | Exam 1 covering Chapters 1-4. Study guide pdf | |
| 18 | 10/5 | 6 | Complex series. |
| 19 | 10/7 | 6 | Power series. |
| 20 | 10/9 | 6 | Differentiating power series. |
| 21 | 10/12 | 7 | Exponential, trigonometric and hyperbolic functions. |
| 22 | 10/14 | 7 | Exponential, trigonometric and hyperbolic functions. |
| 23 | 10/16 | 7 | Hw discussion. Argument, logarithm, and powers. |
| 24 | 10/19 | 7,8 | Holomorphic branches of logarithm
and nth root. Conformal mappings. |
| 25 | 10/21 | 8 | Conformal mappings. |
| 26 | 10/23 | 8 | Hw discussion. Conformal mappings. |
| 27 | 10/26 | Riemann Mapping Theorem -- a discussion. | |
| 28 | 10/28 | 10 | Integration along path. |
| 29 | 10/30 | 10 | Fundamental Theorem of Calculus and examples. |
| 30 | 11/2 | 10,11 | Estimation theorem. Cauchy's Theorem for a triangle. |
| 31 | 11/4 | Problems from Chapters 5-8. | |
| 32 | 11/6 | Exam 2 covering Chapters 5-8. Study guide pdf | |
| 33 | 11/9 | 11 | Antiderivative and Cauchy's theorems for a convex region. |
| 34 | 11/11 | 12 | Cauchy's and Antiderivative theorems for a simply connected region. |
| 35 | 11/13 | 13 |
Cauchy's Theorem for a multiply connected region. Cauchy's Integral formula. |
| 36 | 11/16 | 13 | Liouville's Theorem. The Fundamental Theorem of Algebra. |
| 37 | 11/18 | 13 | Cauchy's formula for the derivatives. |
| 38 | 11/20 | 14 | Taylor's Theorem. |
| 39 | 11/30 | 15 | Zeros of holomorphic functions. |
| 40 | 12/2 | 15, 17 | Identity Theorem. Laurent series. |
| 41 | 12/4 | 17 | Laurent's Theorem. Estimates for the coefficients. Singularities. |
| 42 | 12/7 | 17 | Classification of isolated singularities. |
| 43 | 12/9 | 18 | Residues. Cauchy's residue theorem. |
| 44 | 12/11 | Review | |
Final Exam: Tuesday, December 15, 10:10 a.m. - noon, in 201 Osmond. Study guide pdf