## Equations in Mathematical Physics: A practical courseMany physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers. |

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### Contents

Introduction | 1 |

Chapter 1 Elliptic problems | 7 |

Chapter 2 Hyperbolic problems | 81 |

Chapter 3 Parabolic problems | 161 |

205 | |

207 | |

### Other editions - View all

Equations in Mathematical Physics: A practical course Victor P. Pikulin,Stanislav I. Pohozaev Limited preview - 2012 |

Equations in Mathematical Physics: A practical course V.P. Pikulin,Stanislav I. Pohozaev Limited preview - 2013 |

### Common terms and phrases

arbitrary constants Bessel function boundary conditions boundary value problem C1 and C2 C2 are arbitrary Cauchy problem circular cylinder coefficients const denotes Dirichlet problem disc eigenfunctions eigenvalues equal to zero equation utt Example expression in equation Figure Find the solution Find the steady Find the temperature following boundary value following mixed problem formula Fourier transformation Green function half—plane half—space heat equation Helmholtz equation homogeneous hyperbolic inﬁnite initial conditions initial temperature Laplace equation Laplace transformation maintained at temperature mathematical membrane Neumann problem null boundary conditions obtain ordinary differential equation original problem oscillations partial differential equation particular solutions Poisson equation potential problem is given satisﬁes seek the solution separation of variables sinh solution atoms solution of equation solution of problem Solve the boundary Solve the Cauchy Solve the Dirichlet Solve the following Substituting this expression temperature zero wave equation whence