Math 421: Complex Variables, Spring 2025

Instructor

Weimin Chen, 1323K LGRT wch@umass.edu

Office hours: Thursdays 3-4pm or by appointment.

Lectures: TuTh 1-2:15pm, LGRC A203, 01/30/2025-05/09/2025.

Text

Complex Variables and Applications (Eighth Edition) by James Ward Brown and Ruel V. Churchill

Tentative Schedule

Chapter 1: Complex Numbers

Chapter 2: Analytic Functions

Chapter 3: Elementary Functions

Review. Midterm Exam 1

Chapter 4: Integrals

Chapter 5: Series

Review. Midterm Exam 2

Chapter 6: Residues and Poles

Chapter 7: Applications of Residues

Chapter 8 (if time permits)

Review, Final Exam

Exam Schedule

Midterm 1: March 13, in class.

Midterm 2: April 15, in class.

Final Exam: as scheduled on Spire.

Grading

Midterm 1, 20\%, Midterm 2, 20\%, Final, 30\%, Homework 30\%. (Standard scale for final grade: A: 90\%, B: 80\%, etc.)

Make-up policy

If you have a legitimate (i.e., multiple exams at the same time, medical problems, emergency absences, religious observances) scheduling conflict with any of the exams, please notify me of the conflict as soon as you become aware of it. Please note that previously arranged travel plans are not a valid reason to be given a make-up exam.

Use of Calculators

Calculators are useful auxiliary tools for the course. However, it will be expected that you can work all of the problems without the aid of a calculator. Calculators will be permitted on the exams, but it will be expected that all non-arithmetic work is present and explained in your answer.

Homework

Homework is collected and graded on a (roughly) weekly basis. (Time of collection: TBA.) Each homework must be well organized and neatly written. Homework assignments will be posted at the bottom of this page (please check often). We plan to use Gradescope. Homework will be graded by a special grader.

Announcement

Welcome to the class!

Some practice problems for the Midterm 1 on March 13.

Some practice problems for the Midterm 2 on April 15.

Required Syllabus Statements

University policies regarding Accommodations, Academic Honesty, and Title IX, apply to all courses. The policies can be found below. Required Syllabus Statements

Homework Assignments

Note: The dates marked with a star are special dates.
Hw # Assignments Due date
1 #1(a), #2 in page 5, #1 in page 8, #1(a),(d), #5 in page 12, #1(b),(d) in page 14, #4,#6,#7 in page 15, #1 in page 22, #5 in page 23. 2/16*
2 #3,#4,#5 in page 30, #1,#3,#7 in page 44, #1,#3,#5 in page 55, #10, #11 in page 56. 2/20
3 #1(a),(c), #4 in page 62, #8,#9 in page 63, #1(c),(d), #2(d), #3(c),#4(c) in page 71, #1(c),#2(a) in page 77, #6,#7 in page 78. 3/4
4 #1(b) in page 81, #3, #7 in page 82, #3, #6, #9 in page 97, #1,#6,#9 in page 104, #11, #12, #13 in page 109. 3/14
5 #2(b), (c), #4 in page 121, #5, #6 in page 126, #1, #2, #3, #6 in page 135, #7,#8 in page 136. 3/28
6 #2, #4, #5 in page 149, #1 in page 160, #2, #4 in page 161, #1(a), (b), #2 in p. 170, #4, #7, #8 in p.171. 4/4
7 #2, #3, #9, in p. 188, #2,#3,#7, in p.196, #13 in p.197, #1, #2 in p.205, #4,#5, #6 in p.206. 4/17