MAT 342 - Applied Complex Analysis - Fall 2022

Lectures: MWF 10:30-11:25pm in Earth & Space 131

Office hours: MF 9-10am, or by appointment

Office: Math Tower 3-118

Course Syllabus

Schedule:

Week # Week of Topics covered

#1    8/22 Complex numbers

#2    8/29 Functions, mappings, limits & derivatives

#3    9/5 Cauchy-Riemann Equations, Analytic functions, harmonic functions

#4    9/12 The exponential function and examples

#5    9/19 Contour integrals

#6    9/26 Antiderivatives and Cauchy–Goursat

#7    10/3 Cauchy-Goursat, Cauchy's Formula, and the max mod principle

#8    10/10 Liouville's Theorem, Fundamental Theorem of Algebra Series, Taylor Series

#9    10/17 Taylor Series and Laurent Series

#10    10/24 Laurent Series and Residues

#11   10/31 Residues, poles, and zeros

#12    11/7 Applications of residues

#13    11/14 Applications of residues & some mappings

#14    11/21 Mappings

#15    11/28 Conformal mappings

#16    12/5 Final Review

Homework:

Homework 1, due August 31

Homework 2, due September 7

Homework 3, due September 14

Homework 4, due September 21

Homework 5, due October 5

Homework 6, due October 12

Homework 7, due October 19

Homework 8, due October 26

Exams:

Midterm 1: Friday September 23rd (?)

Midterm 2: Friday October 28th (?)

Final Exam: 2:15-5:00 PM, Wednesday

December 14, 2022