## Math 417 Complex Analysis with Applications Fall 2019

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, coskun@math.uic.edu

Office hours: MWF 9-10 and by appointment in SEO 423

Venue: Lecture Center A 002 (Note new classroom!)

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.

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.

Grading: There will be two midterm exams and a final examination. The midterms and the homework will each count for 20% of your grade. The final examination will account for 40% of your grade. In addition, you can write a 7-10 page paper on the applications of complex analysis to your field of specialty to count for 20% of your grade. In order to pass the course, you must pass the final exam.

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 on the web. I encourage you to explore them.

Course materials:

• The syllabus (pdf).
• Homework 1, due Wednesday September 4 (pdf)
• Homework 2, due Wednesday September 11 (pdf)
• Homework 3, due Wednesday September 18 (pdf)
• Homework 4, due Wednesday September 25 (pdf)
• Homework 5, due Wednesday October 2 (pdf)
• Homework 6, due Wednesday October 9 (pdf)
• Practice mideterm: Last semester's midterm (pdf)
• Practice midterm: (pdf)
• MIDTERM 1 (pdf)
• Homework 7, due Wednesday October 23 (pdf)
• Homework 8, due Wednesday October 30 (pdf)
• Homework 9, due Wednesday November 6 (pdf)
• Homeowork 10, due Wednesday November 13 (pdf)
• Practice Midterm (pdf)
• Second Midterm, due Wednesday November 20 (pdf)
• Homeowork 11, due Wednesday November 27 (pdf)
• Final, Due Wednesday December 4 (pdf)
• Homework 12, Not to be turned in (pdf)