Mixed Boundary Value Problems - Duffy, Dean G.

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Résumé :
This book covers the various methods used to solve mixed boundary value problems. It uses MATLAB? to illustrate the solutions and contains the code so readers can reproduce some of the examples. The author provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve a variety of mixed boundary value problems using separation of variables, transform methods, the Wiener-Hopf technique, Green's function, and conformal mapping....

Sommaire:
Overview Examples of Mixed Boundary Value Problem Integral Equations Legendre Polynomials Bessel Functions Historical Background Nobili's Rings Disc Capicator Another Electrostatic Problem Griffith Cracks The Boundary Value Problem of Reissner and Sagoci Steady Rotation of a Circular Disc Separation of Variables Dual Fourier Cosine Series Dual Fourier Sine Series Dual Fourier-Bessel Series Dual Fourier-Legendre Series Triple Fourier Sine Series Transform Methods Dual Fourier Integrals Triple Fourier Integrals Dual Fourier-Bessel Integrals Triple and Higher Fourier-Bessel Integrals Joint Transform Methods The Wiener-Hopf Technique The Wiener-Hopf Technique When the Factorization Contains No Branch Points The Wiener-Hopf Technique When the Factorization Contains Branch Points Green's Function Green's Function with Mixed Boundary Value Conditions Integral Representations Involving Green's Functions Potential Theory Conformal Mapping The Mapping z = w + alog(w) The Mapping tanh[piz/(2b)] = sn(w, k) The Mapping z = w + lambda w2 - 1 The Mapping w = ai(z - a)/(z + a) The Mapping z = 2[w - arctan(w)]/pi The Mapping kw sn(w, kw) = kz sn(Kzz/a, kz) Index