Complex Variables

Time and Location

MWF Period 8 in 217 Little Hall

Office hours

To be arranged

Text

Brown and Churchill – Complex Variables with Applications, Edition 9

Topics

Consider the real-valued function f of a real variable defined by the rule f(x) = 1/(1 + x^2). How nice is this function? Bounded? Check. Goes to zero ‘at infinity’? Check. Continuous? Check. Differentiable? Check. Twice differentiable? Check. Differentiable to all orders? Check. All the derivatives go to zero ‘at infinity’? Check. Pretty nice, surely. So why does its Taylor series about the origin only have 1 as its radius of convergence?

Among many other things, in this course we shall see that an answer to this question lies outside the real numbers: in the complex plane. Complex analysis is both central to mathematics and a source of numerous applications. A single undergraduate course cannot hope to do more than simply scratch the surface of this deep subject: one of the more famous researchers in
complex analysis once said that he had spent most of his professional life in the unit disc in the complex plane!

The course will address material primarily from the first seven chapters of the adopted text (approximately two-thirds of the book). However, we shall not work through every one of the ninety-five sections contained therein; omitted sections will be announced in advance. Moreover, we shall look at occasional topics that are not to be found in the text; for these, separate notes will be posted to Canvas.

Details regarding such matters as testing and grading will be announced at the start of semester.

Policies

For various matters of policy, please consult ‘Policies plus’ at the Files page.