M361: Theory of Functions of a Complex Variable

Unique ID

56650

Course time

Tuesday, Thursday, 11 a.m.–12:30 p.m.

Course location

RLM 5.118

Instructor

Samuel Isaacson

Office

RLM 11.164

Office hours

• Tuesday, 1:30–3 p.m.
• Wednesday, 2:30–4 p.m.
• By appointment

Email

isaacson@math.utexas.edu

Textbook

Brown, James and Ruel Churchill. Complex Variables and Applications. 8th ed. Boston: McGraw-Hill Education, 2009.

Prerequisites

This course requires M427K or M427L with a grade of at least C or consent of the instructor.

Homework

There will be 5 homework assignments; see the homework policy below.

Midterm exams

• March 7 during lecture
• April 16 during lecture

Final exam time

Friday, May 10, 9:00 a.m.–12:00 p.m.

Final exam location

TBA

Evaluation

• Homework: 10%
• Midterms: 40% (each is worth 20%)
• Final exam: 50%

Grade scale

This scale is subject to revision.

A	93–100	C	73–76
A−	90–92	C−	70–72
B+	87–89	D+	67–69
B	83–86	D	63–66
B−	80–82	D−	60–62
C+	77–79	F	0–59

Attendance

Attendance is recommended but not required.

Course description

M361 is an introduction to complex analysis. Topics include the theory of complex analytic functions, Cauchy’s integral formula, contour integrals, Laurent expansions, harmonic functions, and conformal mapping.

Textbook

The following textbook is required:

1. Brown, James and Ruel Churchill. Complex Variables and Applications. 8th ed. Boston: McGraw-Hill Education, 2009.

Brown and Churchill is available on reserve at the Kuehne Physics-Math-Astronomy library. I also recommend the following optional references:

2. Cartan, Henri. Elementary Theory of Analytic Functions of One or Several Complex Variables. New York: Dover Publications, 1995.

3. Needham, Tristan. Visual Complex Analysis. New York: Oxford University Press, 1997.

4. Pólya, George, and Gordon Latta. Complex Variables. New York: Wiley, 1974.

5. Stein, Elias M., and Rami Shakarchi. Complex Analysis. Princeton, NJ: Princeton University Press, 2003.

6. Wegert, Elias, and Gunter Semmler. “Phase Plots of Complex Functions: A Journey in Illustration.” Notices of the AMS 58, no. 6 (2011). [PDF]

Homework

Problem sets are worth 10% of your grade. There will be five assignments due over the course of the semester. Homework will be collected at the beginning of lectures. Late homework will not be accepted.

I encourage you to work with other students on homework problems. However, your homework must be in your own words. Write up your homework by yourself; if you worked with anyone on the homework, you must indicate so. See the note below on academic integrity.

Exams

In addition to the final exam, there will be two midterm exams during the semester whose dates are noted above. The midterms will be administered during lectures. The midterms and final are worth 90% of your grade with each midterm worth 20% and the final worth 50%. The final will be cumulative.

Calculators and notes will not be permitted on exams. Bring your UT ID with you to each exam.

If you cannot write an exam, let me know at least two weeks in advance. For each exam, there will be a make-up offered for students who missed the original due to an excused absence or medical emergency. If you cannot write the make-up exam, the exam will be dropped.

Email

If you need to email me regarding this course, please include your EID. I will not discuss grades over email.

Religious holidays

In accordance with UT Austin policy, please notify me at least 14 days prior to the date of observance of a religious holiday. If the holiday conflicts with an exam, I will allow you to write a make-up exam within a reasonable time.

Special needs

Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities at 471-6259 (voice), 232-2937 (video), or http://www.utexas.edu/diversity/ddce/ssd.

Academic integrity

If you work with other students, indicate so on your homework. There is no penalty for working with other students, but you must write up your homework by yourself. You may use a calculator or computer system such as Sage or MATLAB on your homework, but calculators and computers are forbidden on exams. Read the University’s standard on academic integrity found on the Student Judicial Services website.

Electronic course instructor survey

Electronic course instructor surveys (eCIS) will be available for the last two weeks of the semester. During the survey period, you may fill out eCIS on UT Direct.

Course plan and lecture notes

This plan may change as the semester progresses. Lecture notes will be posted periodically.

Important dates