UNIVERSITY OF NOTRE DAME DEPARTMENT OF MATHEMATICS

MATHEMATICS 425 - Complex Analysis SPRING SEMESTER 2000

INSTRUCTOR: Prof. Bei Hu, CCMB 219, Phone: 1-5352.

TEXT: Complex Variables, 2nd edition, by Stephen D. Fisher.

INTRODUCTION: The course will cover the first three chapters. From the title of the course you probably know what we are going to study - the complex number systems, which is built on the imaginary number i, i^{2} = −1. A complex number has the form z = x + iy, where x and y are real. We will study complex functions of the form f(z), the theory about continuous functions, differentiable functions (analytic functions and conformal mappings), rational functions, convergence of power series, etc. It turns out that the calculus over the complex numbers is richer than the real and there are many striking results. Many special integrals in the real variables which are difficult to evaluate can be evaluated using complex integration techniques. There is a wide range of applications, such as the electric and magnetic fields which are described by the Maxwell equations, the wave equations, etc.

HOMEWORK: Homework is an important part of this course: this will be regularly assigned. As you know from experience, doing a lot of exercises will give you more practice and a better understanding of the material. Homework will be worth 50 points.

EXAMS: There will be 3 tests (worth 100 pts. each) and a Final Exam (worth 150 pts.) which will cover the material of the entire course.

Missing a scheduled test without an official excuse will result in a score of zero for that test.

GRADE: Your grade for this course is based on three tests, one final and homeworks for a total of 500 points.

OFFICE HOURS: By appointment.