Handbook of Linear Partial Differential Equations for Engineers and Scientists

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ISBN 9781584882992
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Features

  • Contains over 2,200 linear equations and problems of mathematical physics with solutions
  • Avoids using special terminology, where possible, and presents many results in a simple, schematic format
  • Describes many new exact solutions to various equations and boundary value problems
  • Contains more specific science and engineering equations and problems, including some nonlinear PDEs, than any other book available
  • Presents 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

    Editorial 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