Applied Complex Analysis with Partial Differential EquationsThis 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. |
Contents
Complex Numbers and Functions | 1 |
Analytic Functions | 73 |
Complex Integration | 135 |
Copyright | |
16 other sections not shown
Common terms and phrases
analytic functions antiderivative apply Bessel functions boundary conditions boundary value problem c₁ Cauchy's circle complex numbers compute constant converges uniformly cosh cosine curves defined denote derive differential equation Dirichlet problem evaluate Example Exercise exponential Figure Fourier series Fourier transform ƒ and g ƒ is analytic given graph harmonic conjugate harmonic functions heat Hence Hint identity initial interval inverse isotherms Laplace transform Laplace's equation Laurent series Legendre linear fractional transformation mapping method obtain orthogonality parametrized partial sums path piecewise continuous polynomial power series Project Problem proof properties r₁ radius real number region roots Section series expansion Show sine singularity sinh solution solve Suppose that ƒ Theorem tion unit disk upper half-plane w-plane w₁ x²y y₁ z₁ zero π π ди