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A self-contained presentation of the major areas of complex analysis that are referred to and used in applied mathematics and mathematical physics. Topics discussed include infinite products, ordinary differential equations and asymptotic methods.

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Part of a set of three volumes which explores all aspects of complex analysis, this book covers such topics as the construction of conformal maps and discrete Fourier analysis on a non-specialist level.