| Instructor | Plamen Stefanov |
| Office | MATH 728 |
| stefanov@math.purdue.edu | |
| Meeting | MWF, 9:30 AM - 10:20 AM in WALC 3127 |
| Office Hours | W 2:30-3:30, F 2:00-3:00 |
| Lecture Notes | link |
| Grader | Asini Konpola |
| Book | Michael Taylor, Introduction to Complex Analysis, Graduate Texts in Mathematics, AMS, 2019 Other recommended books: Fisher, Complex Variables and Ahlfors, Complex Analysis |
HW1, due 9/3 (Wed) on Gradescope.
HW2: §1.1: 12; §1.2: 4, 5; §1.3: 1, 3. Due 9/14 (Sun) on Gradescope.
HW3, due 9/21 (Sun) on Gradescope.
HW4: from the online PDF version of the book: pp. 77-79: 1, 4, 6, 9, 10, 12; pp. 83-85: 1, 4, 9; pp. 94-96: 8. Due 9/28 (Sun) on Gradescope.
HW5: from the online PDF version of the book: pp. 101: 1, 2, 4, 7, 8, and this question; Due 10/12 (Sun) on Gradescope.
Exam 1: Thu 09/25, 8:00p - 9:30p in LWSN B151 Will cover 1.1-1.5, 2.1-2.3.
Practice Problems: Fisher: pp.53-56, 1-28; pp.73-74: 7, 8, 16; pp. 85-86: 20, 22; pp.133-134: 18, 19, 20, 21.
Exam 2: Thu 10/30, 8:00p - 9:30p in LWSN B151
Final exam: Mon 12/15, 1:00p - 3:00p, WALC 3127
Your course grade will be determined using the following distribution: HW: 1/3; Midterm 1/6 each (1/3 total); Final: 1/3.
Chapter 1: Basic Calculus in the Complex Domain
1.1. Complex numbers, power series, and exponentials
1.2. Holomorphic functions, derivatives, and path integrals
1.3. Holomorphic functions defined by power series
1.4. Exponential and trigonometric functions: Euler’s
formula
1.5. Square roots, logs, and other inverse functions
Chapter 2: Going deeper – the Cauchy integral theorem and consequences
2.1. The Cauchy integral theorem and the Cauchy integral
formula
2.2. The maximum principle, Liouville’s theorem, and the
fundamental theorem of algebra
...