18.112 Functions of a Complex Variable

Class Info

Studies the basic properties of analytic functions of one complex variable. Conformal mappings and the Poincare model of non-Euclidean geometry. Cauchy-Goursat theorem and Cauchy integral formula. Taylor and Laurent decompositions. Singularities, residues and computation of integrals. Harmonic functions and Dirichlet's problem for the Laplace equation. The partial fractions decomposition. Infinite series and infinite product expansions. The Gamma function. The Riemann mapping theorem. Elliptic functions.

This class has 18.06, 18.700, 18.701, 18.100A, 18.100B, 18.100P, and 18.100Q as prerequisites.

18.112 will be offered this semester (Fall 2019). It is instructed by A. Borodin.

This class counts for a total of 12 credits.

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