### Features

Contains over 2,200 linear equations and problems of mathematical physics with solutionsAvoids using special terminology, where possible, and presents many results in a simple, schematic formatDescribes many new exact solutions to various equations and boundary value problemsContains more specific science and engineering equations and problems, including some nonlinear PDEs, than any other book availablePresents solutions to numerous problems related to heat and mass transfer, wave theory, acoustics, elasticity, hydrodynamics, electrostatics, quantum mechanics, and other fields of science and engineering
### Summary

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

### Reviews

"… one-stop shopping for scientists and engineers who need a cookbook solution for partial differential equations. The logical organization--by type of equation…and number of variables--makes finding entries easy. … This very useful book has no competitors."

-CHOICE, October 2002

"…a good example of a reference information resource named 'Handbook.' It is an information tool: comprehensive, condensed, descriptive in 'Contents,' authoritative, and practical. …In one volume it contains over 2,000 solutions to linear partial differential equations …It is not a solution manual to accompany a textbook, but an information resource of advanced level for professionals… a great addition for research and academic collections."

E-Streams, Vol. 6, No. 2

"…I have been reading the Polyanin books "Handbook of Linear Partial Differential Equations for Engineers and Scientists" and "Handbook of Exact Solutions for Ordinary Differential Equations". I think these books are extraordinary, and are destined to become classics … CRC Press has provided an invaluable service to science and engineering by publishing these books."

- William Schiesser, Lehigh University