Handbook of Linear Partial Differential Equations for Engineers and Scientists
1st Edition
Published on 28. November 2001
Book
Hardback
800 pages
978-1-58488-299-2 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
Researchers, university professors, engineers, and students in various fields of applied mathematics, mechanics, physics, control theory, and engineering sciences.
Dimensions
Height: 246 mm
Width: 171 mm
Weight
1520 gr
ISBN-13
978-1-58488-299-2 (9781584882992)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Andrei D. Polyanin | Vladimir E. Nazaikinskii
Handbook of Linear Partial Differential Equations for Engineers and Scientists
Book
01/2016
2nd Edition
CRC Press
€308.50
Article not available at the moment
Content
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
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