Applied and Computational Complex Analysis, Volume 3: Discrete Fourier Analysis, Cauchy Integrals, Construction of Conformal Maps, Univalent FunctionsPresents 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. |
Contents
Discrete Fourier Analysis | 1 |
Cauchy Integrals | 87 |
Potential Theory in the Plane | 214 |
4 | 243 |
6 | 255 |
Simply Connected Regions | 323 |
Construction of Conformal Maps for Multiply Connected | 444 |
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Applied and Computational Complex Analysis, Volume 3: Discrete Fourier ... Peter Henrici Limited preview - 1993 |
Common terms and phrases
algorithm analytic function annulus approximation arbitrary assume B₁ boundary correspondence function boundary values bounded Cauchy integral closure complex compute condition conformal mapping conjugate harmonic function constant construct convergence convolution defined denote derivative differential Dirichlet problem discrete Fourier transform doubly connected region evaluated EXAMPLE exists exterior Faber finite follows Fourier coefficients Fourier series function f given hence Hilbert transform Hölder condition Hölder continuous holds integral equation interior inverse Jordan curve kernel Koebe L₂(R Laurent series Lemma Let f linear logarithmic mapping function method modulus Neumann numerical obtain parameter piecewise analytic Poisson's Poisson's equation principal value Privalov problem proof quadrilateral real function representation result Riemann satisfies sequence simply connected simply connected region singularity solution solves Symm's t₁ Theorem uniformly unique unit disk yields zero дп