MATH 3X03, Winter 2019
COMPLEX ANALYSIS I
In this course you will learn the fundamental ideas and surprising results in the study of functions of a complex variable. Once a complex function is differentiable it satisfies a whole range of magical properties: surprising identities relating its integrals and derivatives; you can count its zeros by calculating an integral; the level curves form orthogonal webs; and you can turn the plane into the sphere. By opening up to complex values, you will solve problems involving real variables and functions, which seemed impossible from the real number point of view. Topics include analytic functions, series, residue theorem, conformal maps with applications.
INSTRUCTOR: E. Sawyer
Analytic functions, Cauchy’s theorem, Cauchy’s integral formula, residues, zeroes of analytic functions; Laurent series, the maximum principle.
Three lectures, one tutorial; one term
Prerequisite(s): MATH 2R03 and 2XX3
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS