Math 417 Complex Analysis with Applications Fall 2021

Welcome to Math 417! This course is an introduction to Complex Analysis. Complex Analysis is one of the great subjects of modern mathematics and an invaluable tool in physics and engineering. In this course we will explore the basic properties of complex analytic functions and conformal maps.

Lecturer: Izzet Coskun, icoskun@uic.edu

Time: 11:00-11:50 MWF

Dropin hours: M 1-3 (this will be on zoom)

Venue: Addams Hall 306

Text book: Complex variables and applications by J.W. Brown and R.V.Churchill, McGraw Hill, 2004, Seventh Edition. All page numbers below refer to this book. You may use a different edition or an equivalent text book.

Prerequisites: A solid background in basic analysis including the concepts of limits, continuity, differentiability, Riemann integrals and line integrals. I will assume that you are comfortable with writing proofs.

Homework: There will be weekly homework. The homework is due on Wednesdays at the beginning of class. Late homework will not be accepted. You are allowed to discuss problems; however, the write-up must be your own and should reflect your own understanding of the problem. Three of the homeworks will be special (Midterm I, II and Final). These will be slighly longer, cumulative and you will be required to do on your own.

Grading: Your grade will be entirely based on the homework. The three longer homework sets (Midterms I,II and Final) will each account for 20% of your grade. The regular homework exercises will account for 40% total. In addition, you can write an optional 7-10 page paper on the applications of complex analysis to your field of specialty. A well-written paper will increase your grade by one letter grade.

Additional references: There are many excellent text books in Complex Analysis. You might want to refer to them for more information or a different point of view. Some of my favorites are:

• L. Ahlfors, Complex Analysis, McGraw-Hill 1979.
• K. Knopp, Elements of the theory of functions, Dover 1952.
• K. Knopp, Theory of functions parts I and II, Dover 1996.
• R. Remmert, Theory of complex functions, Springer Graduate Texts in Mathematics.
• T. Needham, Visual complex analysis, Oxford University Press.
• J. B. Conway, Functions of one complex variable, Springer-Verlag, 1978.

Links to other complex analysis webpages: Caution I have not checked the material in these pages. Some seem to have beautiful pictures and applications.

• The complex analysis webpage of John Mathews at Fullerton (html)
• Complex Analysis notes by Paul Scott at the University of Adelaide (html)
• OCW Complex Analysis Webpage at MIT (html)
• There are many other lecture notes and videos on the web. I encourage you to explore them.

Course materials: