Handbook of Linear Partial Differential Equations for Engineers and Scientists

Following 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. Parabolic, hyperbolic, and elliptic equations with constant and variable coefficients New exact solutions to linear equations and boundary value problems Equations and problems of general form that depend on arbitrary functions Formulas for constructing solutions to nonhomogeneous boundary value problems Second- and higher-order equations and boundary value problems An introductory section outlines the basic definitions, equations, problems, and methods of mathematical physics. It also provides useful formulas for expressing solutions to boundary value problems of general form in terms of the Green's function. Two supplements at the end of the book furnish more tools and information: Supplement A lists the properties of common special functions, including the gamma, Bessel, degenerate hypergeometric, and Mathieu functions, and Supplement B describes the methods of generalized and functional separation of variables for nonlinear partial differential equations.

Table of Contents:
INTRODUCTION: SOME DEFINITIONS, FORMULAS, METHODS, AND SOLUTIONS Classification of Second Order Partial Differential Equations Basic Problems of Mathematical Physics Properties and Particular Solutions of Linear Equations Separation of Variables Method Integral Transforms Method Representation of the Solution of the Cauchy Problem via the Fundamental Solution Nonhomogeneous Boundary Value Problems with One Space Variable Nonhomogeneous Boundary Value Problems with Many Space Variables Construction of the Green's Functions: General Formulas and Relations Duhamel's Principles in Nonstationary Problems Transformation Simplifying Initial and boundary Conditions EQUATIONS OF PARABOLIC TYPE WITH ONE SPACE VARIABLE Constant Coefficient Equations Heat Equation with Axial or Central Symmetry and Related Equations Equations Containing Power Functions and Arbitrary Parameters Equations Containing Exponential Functions and Arbitrary Parameters Equations Containing Hyperbolic Functions and Arbitrary Parameters Equations Containing Logarithmic Functions and Arbitrary Parameters Equations Containing Trigonometric Functions and Arbitrary Parameters Equations Containing Arbitrary Functions Equations of Special Form PARABOLIC EQUATIONS WITH TWO SPACE VARIABLES Heat Equation Heat Equation with a Source Other Equations PARABOLIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Heat Equation Heat Equation with a Source Other Equations with Three Space Variables Equations with n Space Variables HYPERBOLIC EQUATIONS WITH ONE SPACE VARIABLE Constant Coefficient Equations Wave Equation with Axial or Central Symmetry Equations Containing Power Functions and Arbitrary Parameters Equations Containing the First Time Derivative Equations Containing Arbitrary Functions HYPERBOLIC EQUATIONS WITH TWO SPACE VARIABLES Wave Equation Nonhomogeneous Wave Equation Telegraph Equation Other Equation with Two Space Variables HYPERBOLIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Wave Equation Nonhomogeneous Wave Equation Telegraph Equation Other Equations with Three Space Variables Equations with n Space Variables ELLIPTIC EQUATIONS WITH TWO SPACE VARIABLES Laplace Equation Poisson Equation Helmholtz Equation Other Equations ELLIPTIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Laplace Equation Poisson Equation Helmholtz Equation Other Equations Equations with n Space Variables HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS Third Order Partial Differential Equations Fourth Order One-Dimensional Nonstationary Equations Two-Dimensional Nonstationary Fourth Order Equations Fourth Order Stationary Equations Higher Order Linear Equations with Constant Coefficients Higher Order Linear Equations with Variable Coefficients SUPPLEMENT A: Special Functions and Their Properties SUPPLEMENT B: Methods of Generalized and Functional Separation of Variables in Nonlinear Equations of Mathematical Physics REFERENCES INDEX