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Handbook of Linear Partial Differential Equations for Engineers and Scientists

Handbook of Linear Partial Differential Equations for Engineers and Scientists


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About the Book

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 problemsAn 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

Review :
"one-stop shopping for scientists and engineers who need a cookbook solution for partial differential equations. The logical organization--by type of equationand 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


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Product Details
  • ISBN-13: 9781584882992
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: Chapman & Hall/CRC
  • Height: 246 mm
  • No of Pages: 800
  • Returnable: N
  • Width: 174 mm
  • ISBN-10: 1584882999
  • Publisher Date: 28 Nov 2001
  • Binding: Hardback
  • Language: English
  • No of Pages: 800
  • Weight: 1520 gr


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Handbook of Linear Partial Differential Equations for Engineers and Scientists
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Handbook of Linear Partial Differential Equations for Engineers and Scientists
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