MATH 4200 Intro to Complex Variables (Fall 2024)

Instructor
Daniel Gulotta, dgulotta@math.utah.edu
Location and time
MWF 11:50am-12:40pm in LCB 215
Course Description
Complex functions and their differentiability, complex integrals, power series, the Cauchy theorem and formulas, residues and applications to evaluating integrals, conformal mappings and applications.
Prerequisites
“C” or better in MATH 3220
Credits
3
Textbook
Complex Variables by Joseph L. Taylor.
Canvas
To access Canvas, visit https://utah.instructure.com. Canvas will be used for announcements, homework assignments and other course materials, and grades.
Office hours
time TBA in JWB 106
Grading
The following categories contribute to the course grade.
Homework 1/3
Exams 1/3
Final 1/3

Grading is according to the following scale.

93% 86% 80% 77% 74% 68% 60% 55% 50% else
A A- B+ B B- C+ C C- D E

The scale is subject to change. If I make changes to the scale, it will only be in your favor.

Exams
The dates of the midterm exams are shown in the schedule below. If you need to miss an exam for a university-approved reason, please contact me at least a week in advance to make alternate arrangements.
Final exam
The final exam will be held on Friday, December 13, 10:30am-12:30pm in LCB 215.
Homework
Homework will be due Mondays at 11:59pm. Homework should be uploaded to the Gradescope tab in Canvas. The lowest two homework scores will be dropped. You may discuss the problems with other students, but you should write up solutions in your own words. You are not allowed to post the questions to online tutoring or question answering services such as Chegg. Depending on the number of students in the class, I may not grade every problem, but I will post solutions to every problem.
Late assignments
Late assignments can be accepted if you make prior arrangements with me, or in the case of emergencies. Otherwise they are not accepted.

Tentative Schedule

Date Topic Textbook HW Due
8/19 Introduction, complex numbers, sequences 1.1
8/21 Sequences and series 1.2
8/23 Exponential function 1.3
8/26 Polar form of complex numbers, logarithm 1.4 #1
8/28 Continuous functions 2.1
8/30 The complex derivative 2.2
9/4 The complex derivative 2.2 #2
9/6 The complex derivative 2.2
9/9 Contour integrals 2.3 #3
9/11 Contour integrals 2.3
9/13 Contour integrals 2.4
9/16 Cauchy’s intergral theorem 2.5 #4
9/18 Cauchy’s integral formula 2.6
9/20 Cauchy’s integral formula 2.6
9/23 Uniform convergence 3.1 #5
9/25 Midterm exam 1
9/27 Uniform convergence 3.1
9/30 Power series 3.2 #6
10/2 Power series 3.2
10/4 Power series 3.2
10/14 Liouville’s theorem 3.3 #7
10/16 Liouville’s theorem 3.3
10/18 Zeros and singularities 3.4
10/21 Maxmimum modulus principle 3.5 #8
10/23 Singularities 3.4
10/25 Laurent series 4.3
10/28 Laurent series 4.3 #9
10/30 Residue theorem 4.4
11/1 Residue theorem 4.4
11/4 Rouché theorem 4.5 #10
11/6 Midterm exam 2
11/8 Rouché theorem 4.5
11/11 Computation of residues 5.1 #11
11/13 Integrals via residues 5.2
11/15 Summation of infinite series 5.5
11/18 Summation of infinite series 5.5 #12
11/20 Fourier series 5.3
11/22 Conformal mappings 6.1
11/25 Riemann sphere, Mobius transformations 6.2-6.3 #13
11/27 Riemann sphere, Mobius transformations 6.2-6.3
12/2 Riemann sphere, Mobius transformations 6.2-6.3 #14
12/4 Riemann mapping theorem 6.4

Student Information

The Americans with Disabilities Act (ADA): The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities.

All written information in this course can be made available in an alternative format with prior notification to the Center for Disability & Access (CDA). CDA will work with you and the instructor to make arrangements for accommodations. Prior notice is appreciated. To read the full accommodations policy for the University of Utah, please see Section Q of the Instruction & Evaluation regulations.

In compliance with ADA requirements, some students may need to record course content. Any recordings of course content are for personal use only, should not be shared, and should never be made publicly available. In addition, recordings must be destroyed at the conclusion of the course.

If you will need accommodations in this class, or for more information about what support they provide, contact:

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Plagiarism and cheating are serious offenses and may be punished by failure on an individual assignment, and/or failure in the course. Academic misconduct, according to the University of Utah Student Code:

“…Includes, but is not limited to, cheating, misrepresenting one’s work, inappropriately collaborating, plagiarism, and fabrication or falsification of information…. It also includes facilitating academic misconduct by intentionally helping or attempting to help another to commit an act of academic misconduct.”

For details on plagiarism and other important course conduct issues, see the U’s Code of Student Rights and Responsibilities.