132. Complex Analysis for Applications. Lecture, three hours; discussion, one hour. Prerequisites: courses 32B, 33B. Introduction to basic formulas and calculation procedures of complex analysis of one variable relevant to applications. Topics include Cauchy-Riemann equations, Cauchy integral formula, power series expansion, contour integrals, residue calculus.

Complex analysis is one of the most beautiful areas of pure mathematics, at the same time it is an important and powerful tool in the physical sciences and engineering. The course Math 132 is aimed primarily at students in applied mathematics, engineering, and physics, and it is satisfies a major requirement for students in Electrical Engineering.

The topics covered in Math 132 include: analytic functions, Cauchy-Riemann equations, harmonic functions, branch points, branches of multiple-valued functions, Cauchy's theorem, integral representation formulae, power series of analytic functions, zeros, isolated singularities, Laurent series, poles, residues, use of residue calculus to evaluate real integrals, use of argument principle to locate zeros, fractional linear transformations, and conformal mapping.

Students entering Math 132 are assumed to have some familiarity with complex numbers from high school, including the polar form of complex numbers. Students in Math 132 are also assumed to have a strong background in single and multivariable calculus, including infinite series, power series, radius of convergence (ratio and root tests), integration term by term of power series, parametrized curves, line integrals, and Green's theorem. Some of this material is reviewed in Math 132, though at a fast pace.

Several sections of Math 132 are offered each term.