| 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.
HW6: from the online PDF version of the book: pp. 123: 1, 2; pp. 128-129: 4; pp. 133-134: 1-3, 4. Due 10/21 (Tue) on Gradescope.
HW7: from the PRINTED version of the book: pp. 193-194: 1, 2, 6, 7, 8. Due 10/28 (Tue) on Gradescope.
HW8: from the online version of the book: pp. 201: 1,2 (you can do #1 it with trigonometry); p.207: 1, ... [more to follow, I need to cover more stuff first] Due ??? 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. Will cover 2.4 - 2.8; 4.1 - 4.3 (only the part of 4.3 I covered)
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
2.3. Harmonic functions on planar domains
2.4. Morera’s theorem, the Schwarz reflection principle, and
Goursat’s theorem
2.5. Infinite products
2.6. Uniqueness and analytic continuation
2.7. Singularities
2.8. Laurent series
Chapter 4: Residue calculus, the argument principle, and two very
special functions
4.1. Residue calculus
4.2. The argument principle
4.3. The Gamma function (a part of it)
4.4. ...
4.5. ...
4.6. ...
4.7. ...
4.8. ...