The theory of calculus with complex numbers, also known as the theory of functions of a complex variable,
is the most original creation of nineteenth century mathematics and has been acclaimed as one of the most
harmonious theories in the abstract sciences.
Complex function theory is not just a simple extension of the real theory to the complex numbers — the condition of complex differentiability imposes strong requirements, and complex analytic functions behave much better than their real counterparts.
Besides uncovering their beautiful geometry and remarkable properties, the study of complex analytic functions illuminates the theory of functions of a real variable, and allows us to solve many real integrals otherwise beyond the reach of our techniques.
This course is an introduction to complex analysis, intended for students in Mathematics, Physics, and Mathematics and Engineering. We will focus on a careful development of the theory as well as some applications to physical problems.
|Instructor: Mike Roth|
|Office Hours: Fridays, 9:30—11:30, Jeff 507|
|Textbook: Fundamentals of Complex Analysis, by Edward Saff and Arthur Snider, 3rd edition.|
|Classes (slot 2)|
|Mon. 9:30—10:30||Wed. 8:30—9:30||Thurs. 10:30—11:30|
|All classes, and the tutorial, are in Stirling A.|
There are twelve homework assignments during the semester. The lowest two of these twelve grades will be dropped when computing the homework grade for the course.
|Midterm||Oct. 28||19:45—21:45||Ellis Auditorium|
|Final||Dec. 7||14:00—17:00||Grant Hall|