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18.112 Functions of a Complex Variable

Prereq: 18.100A, 18.100B, 18.100P, or 18.100Q; 18.06, 18.700, or 18.701
U (Fall)
12 Units

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.

A. Borodin

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Subject meets with 18.1121

Subjects

http://catalog.mit.edu/subjects/

...GIR): 18.02 , 18.02A , 18.022 Chemistry (GIR): 3.091 , 5.111 , 5.112...

Subjects

http://catalog.mit.edu/summer/subjects/

...GIR): 18.02 , 18.02A , 18.022 Chemistry (GIR): 3.091 , 5.111 , 5.112...

General Institute Requirements

http://catalog.mit.edu/mit/undergraduate-education/general-institute-requirements/

...term: 18.02 , the basic version, and 18...5.111 and 5.112 emphasize basic chemical...

Department of Mechanical Engineering

http://catalog.mit.edu/schools/engineering/mechanical-engineering/

...in those programs. 1 18.032 Differential Equations...Graduate Office , Room 1-112, 617-253-2291...

Department of Chemical Engineering

http://catalog.mit.edu/schools/engineering/chemical-engineering/

...as 5.111 / 5.112 Principles of Chemical...60 Thermodynamics and Kinetics , 18.03 Differential Equations...