Handbook of Linear Partial Differential Equations for Engineers and ScientistsFollowing in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. |
Contents
Introduction | 1 |
1 Parabolic Equations with One Space Variable | 43 |
2 Parabolic Equations with Two Space Variables | 161 |
3 Parabolic Equations with Three or More Space Variables | 205 |
4 Hyperbolic Equations with One Space Variable | 279 |
5 Hyperbolic Equations with Two Space Variables | 341 |
6 Hyperbolic Equations with Three or More Space Variables | 393 |
7 Elliptic Equations with Two Space Variables | 467 |
8 Elliptic Equations with Three or More Space Variables | 533 |
9 HigherOrder Partial Differential Equations | 601 |
Supplement A | 655 |
Supplement B | 681 |
| 769 | |
| 777 | |
Other editions - View all
Handbook of Linear Partial Differential Equations for Engineers and Scientists Andrei D. Polyanin No preview available - 2001 |
Handbook of Linear Partial Differential Equations for Engineers and Scientists Andrei D. Polyanin No preview available - 2001 |
Common terms and phrases
A. A. Samarskii A. D. Polyanin A. G. Butkovskiy 1979 A. N. Tikhonov additional term arbitrary constants arbitrary function B. M. Budak boundary condition boundary value problem Carslaw and J. C. Cauchy problem conditions are prescribed considered in Subsection const constant coefficient equation coordinate system corresponding cosh cylinder of finite determined by solving eigenfunctions eigenvalues equation’s nonhomogeneity Exact solution finite length first-order following conditions formula in Paragraph fundamental solution Green’s function H. S. Carslaw heat equation Helmholtz equation homogeneous boundary conditions homogeneous equation infinite initial condition integral J. C. Jaeger Laplace equation leads length is considered M. B. Kapilevich Mixed boundary value modified Bessel functions ordinary differential equations original equation parameter Particular solutions polynomials positive roots rectangle is considered Reference S. G. Mikhlin satisfies Second boundary value sinh solution of equation space variables spherical substitution Third boundary value three-dimensional transcendental equation transformation two-dimensional V. M. Babich