Mixed Boundary Value Problems

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[πz/(2b)] = sn(w, k)
The Mapping z = w + λ√w² - 1
The Mapping w = ai(z - a)/(z + a)
The Mapping z = 2[w - arctan(w)]/π
The Mapping k_w sn(w, k_w) = k_z sn(K_zz/a, k_z)
Index