Math 427: Complex Analysis

Fall 2018

Lectures: MWF 11:30-12:20 in THO 325
Instructor: Jarod Alper (jarod@uw.edu)
Office: PDL C-544
Office hours: Mon, Wed: 4-5

TA: Thomas Lou (lous@uw.edu)
Office hours: Thursday 5-7 pm in PDL C-401
Textbook:
Syllabus: This course is on the calculus of complex functions. We will discuss differentiation and integration of complex-valued functions of a complex variable. Among the topics we will cover are Cauchy's Integral Theorem, Liouville's Theorem, and the Maximum Modulus Principle. We will cover roughly the first three chapters of Taylor's book Complex Analysis.

Homework assignments: There will be regular homework assignments. The lowest homework score will be dropped. Homeworks are due in the beginning of class.


Schedule: The content of the lectures will be posted here. The sections of the textbook quoted below are only a rough approximation of what we actually covered in class.

Lecture Date Topics covered Remarks
Week 1
1 Wed Sept 26 Introduction: complex numbers
2 Fri Sept 28 Convergence of sequences and series
Week 2
3 Mon Oct 1 Complex exponential and polar coordinates
4 Wed Oct 3 Discussion
5 Fri Oct 5 Nth Roots and the complex logarithm HW 1 due
Week 3
6 Mon Oct 8 Topoogy of the complex numbers
7 Wed Oct 10 Discussion
8 Fri Oct 12 Continuous functions HW 2 due
Week 4
9 Mon Oct 15 Multi-valued functions; complex differentation
10 Wed Oct 17 Cauchy-Riemann equations
11 Fri Oct 19 Discussion
Week 5
12 Mon Oct 22 Complex integration and contour integrals HW 3 due
13 Wed Oct 24 Contour integrals
14 Fri Oct 26 Cauchy's Integral Theorem for triangles
Week 6
15 Mon Oct 29 Discussion
16 Wed Oct 31 Cauchy's Integral Theorem for Convex Sets HW 4 due
17 Fri Nov 2 Midterm
Week 7
18 Mon Nov 5 Cauchy's Integral Theorem revisited; Cauchy's Integral Formula
19 Wed Nov 7 Cauchy's Integral Formula and Index functions
20 Fri Nov 9 Properties of the index function
Week 8
Mon Nov 12 No class--Veterans Day
21 Wed Nov 14 Uniform convergence HW 5 due
22 Fri Nov 16 Power series and convergence
Week 9
23 Mon Nov 19 Power series are analytic
24 Wed Nov 21 Discussion
Fri Nov 23 No class--Thanksgiving
Week 10
25 Mon Nov 26 Power series expansions of analytic functions HW 6 due
26 Wed Nov 28 Louiville's theorem and the fundamental theorem of algebra
27 Fri Nov 30 Zeroes of analytic functions
Week 11
28 Mon Dec 3 Singularities of analytic functions
29 Wed Dec 5 Review
30 Fri Dec 7 No class HW 7 due
Final
Wed Dec 12 Final examination, 2:30 - 4:20 pm


Midterm: There will be one in class midterm
Final examination:
Grading: The lowest homework score will be dropped.