Applied Complex Analysis with Partial Differential Equations
This reader-friendly book presents traditional material using a modern approach that invites the use of technology. Abundant exercises, examples, and graphics make it a comprehensive and visually appealing resource. Chapter topics include complex numbers and functions, analytic functions, complex integration, complex series, residues: applications and theory, conformal mapping, partial differential equations: methods and applications, transform methods, and partial differential equations in polar and spherical coordinates. For engineers and physicists in need of a quick reference tool.
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Complex Numbers and Functions
Supplement on Calculus of Functions of Several Variables
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27r-periodic analytic functions antiderivative apply Bessel functions boundary conditions boundary data boundary value problem bounded Cauchy Cauchy-Riemann equations change of variables circle complex numbers complex-valued function compute constant converges uniformly cosh cosine curves defined denote derivative differential equation Dirichlet problem evaluate Example Exercise exponential Figure Fourier coefficients Fourier series Fourier transform function f(z given graph harmonic conjugate harmonic functions heat Hence Hint identity illustrate inside integral formula interval inverse isotherms Laplace transform Laplace's equation Laurent series Lemma linear fractional transformation method Neumann obtain one-to-one orthogonality parametrized partial sums piecewise continuous piecewise smooth Plot Poisson integral Poisson problem polar pole power series Project Problem proof properties prove real line real number region result roots Section sequence series expansion Show sine singularity sinh solution solve Suppose temperature distribution tion unit disk upper half-plane z-plane zero