MAT 514: Analysis for Teachers II

This is a course for students in the teaching masters program, and is an introduction to functions of one complex variable.

Course Details

Instructor: Jack Burkart
Class is Tuesday and Thursday from 1:30-4:55pm. We will take breaks liberally.
Classroom is Earth&Space 181.
My Office is 2-105. Office Hours are Thursdays 12:00-1:00 in 2-105 and Wednesdays from 11:00am-1:00pm in the MLC. Also by appointment/if my door is open.

Textbook and Other Useful References

[BMPS] "A First Course in Complex Analysis". This is our primary reference, and is available freely online here. alternative pdf link

Syllabus

An updated syllabus can be found here.

Term Paper and Presentation

A list of possible term paper and presentation ideas can be found here. These have a big range of difficulty, and you should set up a meeting with me to help decide a good topic. As we go through the class, I may skip more material in the text, and this can make available more project possibilities. Please feel free to make your own suggestions!

Tentative Schedule

Date	Reading	Topic	Homework	Miscellaneous
July 9	[BMPS] 1.1,1.2,1.3	Introduction. Complex Numbers. Basic Topology in the Plane	HW 1 Due July 18	Note the new due date!
July 11		NO CLASS		Class will be made up by adding time to three sessions, dates TBD.
July 16	Review Limits. Review differentiability on R and R^2. [BMPS] 1.4,2.1,2.2.	Some More Topology. Paths. Limits and Continuity. Holomorphic Functions	HW 2 Due July 23
July 18	[BMPS]2.3,2.4,3.1,3.2,3.3	More holomorphic functions. The Cauchy Riemann Equations. The Riemann Sphere.
July 23	[BMPS] 3.4,3.5	Complex versions of familiar functions and wrap up of chapter 3.	Homework 3 due August 1	Midterm topics will be based on material from chapters 1-3.
July 25	Review definition of a line integral, Riemann Integral. [BMPS] 4.1, 4.2.	Conclude discussion of logarithm. Integration of Complex Functions	Practice Midterm
July 30	[BMPS] 4.3, 4.4. Some of Ch. 5.	More integration. Cauchy Integral Formula and its Applications	HW 4 Due August 8	Sample Midterm Solutions and List of known corrrections
Aug. 1	[BMPS] 7.3, 7.4, 8.1, 8.2	Power Series		Midterm: In class 3:30-4:30. Midterm Solutions
Aug. 6	[BMPS] 8.1,8.2	Power Series and Holomorphic functions. Classification of Singularities.	HW5 Due August 15
Aug. 8	[BMPS] Chapter 9	The Residue Theorem and its Applications.
Aug. 13		Presentations.	Practice Final Exam	Note: The final exam will cover material covered in class in chapters 4-9 (Chapter 6 not included).
Aug. 15		Presentations. Final Exam.	Practice Final Solutions	Final Solutions (This link won't work until after the final!)