MAT 345E - Complex Analysis

Course Objectives

Students completing this course will be able to
1. Work with Complex numbers.
2. Be familiar with complex analytic functions and their properties.
3. Understand the similarities and differences between the real and complex elementary functions.
4. Set up and directly evaluate contour integrals or evaluate contour integrals using the Cauchy Integral theorem.
5. Find Taylor or Laurent Series for simple functions. Show understanding of the convergence regions for each type of series.
6. Identify and classify zeros and singular points of functions. Compute residues. Use residues to evaluate various contour integrals.
7. Evaluate improper integrals and definite integrals involving sines and cosines.

Course Description

Complex numbers, analytic and harmonic functions, elementary functions, contour integrals, Cauchy theorem, Cauchy integral formula. Taylor series. Singular and isolated singular points. Laurent series. Residue theorem. Application of Residue theorem to calculation of integrals. Maximum modulus principle.