Applied and Computational Complex Analysis, Volume 3: Discrete Fourier Analysis, Cauchy Integrals, Construction of Conformal Maps, Univalent Functions
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.
Simply Connected Regions
Construction of Conformal Maps for Multiply Connected
Polynomial Expansions and Conformal Maps
2tri Jr algorithm analytic function annulus approximation arbitrary assume boundary correspondence function boundary values bounded Cauchy integral closure complex compute condition conformal mapping conjugate harmonic function constant construct converges 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 Laurent series Lemma Let f linear logarithmic mapping function method modulus 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 ſº Sokhotskyi formulas solution solves Symm's Theorem uniformly unique unit disk yields zero