MAA 4402/5404 COMPLEX VARIABLES SPRING 2026 SYLLABUS

TENTATIVE VERSION

Dr. Frank Garvan

408 Little Hall
(352) 294-2305
fgarvan@ufl.edu

Office Hours (in person and zoom)

Monday 3rd Period (9:35-10:25am) and 7th Period (1:55 – 2:45pm),
Wednesday 9th Period (4:05-4:55pm), and Friday 5th Period (11:45-12:35pm).
To arrange a ZOOM MEETING send email to Dr.G. in advance.

Prerequisites

MAC 2313 or MAC 3474, and MAP 2302, both with minimum grades of C.

Textbook

R.V. Churchill and J.W. Brown, Complex Variables and Applications, 9th Edition, McGraw-Hill.
Students are expected to read the relevant sections of the text in preparation for class and to supplement the material covered in lectures. Reading examples in the textbook is important preparation for doing homework.

Course Description

Complex numbers, analytic functions, Cauchy-Riemann equations, harmonic functions, elementary functions, integration, Cauchy-Goursat theorem, Cauchy integral formula, infinite series, residues and poles, conformal mapping. Credit will be given for, at most, MAA 4402 or MAA 5404.

MAA 5404 Additional Topic: Elliptic Functions (Reading and homework assignment)

Course Objectives and Goals:

• For the student to master the definitions and theory of functions of a complex variable.
• For the student to write clear, complete and logical solutions of problems involving functions of a complex variable.

Tentative Weekly Course Schedule

• WEEKS 1-2: Complex Numbers
• WEEKS 3-4: Analytic Functions
• WEEKS 5-6: Elementary Functions
• WEEKS 7-8: Integrals
• WEEK 9: Series
• WEEKS 10-11: Residues and Poles
• WEEKS 12-13: Applications of Residues

Homework

Every non-exam Friday a portion of class will be devoted to an In-Class Homework Session. In the In-Class Session, students will work together (with Dr.G’s assistance) to check their homework for correctness and evaluate the quality of their proof writing.
After the In-Class sesion a Homework Graded Problem(s) will be released and due the following Monday evening.Homework Assignments consist of three flavors:

1. Suggested Homework Problems. These problems are posted on CANVAS.
   These problems are not collected but doing them will help you master the
   material. Dr.G can check or help with these problems in Office Hours.
2. Weekly Homework Sessions. The weekly homework session problems
   will be posted. The first set of problems will be due the evening of
   Thursday January 22. These problems will be discussed in class the following day
   but not graded, but
   through the review process at the Friday In-Class Homework Session,
   it will be checked for correctness.
3. Graded Homework. There will be weekly Graded Homeworks will be
   posted after each In-Class Homework Session. Graded Homework 1 will be
   posted after the first In-Class Homework Session on Friday January 23 and will be
   due Monday evening January 26, and should be uploaded in CANVAS.Doing all the homework is essential for success in this class as the exams
   test your conceptual understanding of the homework assignments. Some
   homework problems involve elementary proofs. The solution to all homework
   problems should be clear, logical and complete. Students are encouraged
   to check their work with their instructor. See Tokens below.

Daily Quizzes

Short quizzes will be given each day, and graded on a weekly basis.
Each period begins with a Green Quiz posted the previous evening and
ends with a Pink Quiz. Completed quizzes should be uploaded the evening
of each class day.

Assessment

Assessment will be based on the following

Daily Quizzes	5%
Graded Homework	20%
Exams	75%

Exams

• There will be three in class exams. There will some opportunity
  to retake an Exam question. See Tokens below.
• There will be an Optional Comprehensive Final Exam.
  Any missed exam can be replaced by the Optional Comprehensive Exam.
  Lowest exam score can be replaced by the Optional Comprehensive Exam.

Exam Schedule

• Exam 1: Friday, February 13
• Exam 2: Friday, March 13
• Exam 3: Monday, April 20
• Optional Comprehensive Final Exam: Friday, May 1, 7:30 – 9:30 AM

Attendance

Attendance is required.
Over 50% attendance is required for a passing grade.

Grading

Grading scale:

• A (90%); A- (87%); B+ (84%); B (80%); B- (77%); C+ (72%); C (65%); D (55%)

Tokens:

There are 3 ways to earn a Dr. G token: 1) attendance
(white token), 2) coming to office hour (red token), and 3)
homework session problems (blue token).
To earn a blue token one needs to upload completed homework session
problems by 11:59PM Thursday, particpate in the Friday homework session
and complete a group report.
Attendance and Homework tokens can be
picked up during class. Office hour tokens are given when a student
attends an office hour. Tokens can be redeemed after each exam for
the opportunity to redo ONE of the four exam questions. A student
needs 8 white attendance tokens, 2 red office hour tokens, and
2 blue homework tokens in order to redo an EXAM 1 question. Tokens
cannot be “rolled over”, e.g., tokens to redo a question from
Exam 2 must be earned in the period after Exam 1. Required number
of tokens for Exam 2 to be announced later.
Tokens may NOT be shared with other students.

Additional Information on UF Academic Policies and Resources

See
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