Includes bibliographical references and index.
Exact Solutions -- First-Order Equations with Two Independent Variables -- Equations of the Form f(x,y) w/ x + g(x,y) w/ y = 0 -- Equations of the Form f(x,y) w/ x + g(x,y) w/ y = h(x,y) -- Equations of the Form f(x,y) w/ x + g(x,y) w/ y = h(x,y)w -- Equations of the Form f(x,y) w/ x + g(x,y) w/ y = h1(x,y)w + h0(x,y) -- First-Order Equations with Three or More Independent Variables -- Equations of the Form f(x,y,z) w/ x + g(x,y,z) w/ y + h(x,y,z) w/ z = 0 -- Equations of the Form f1 w/ x + f2 w/ y + f3 w/ z = f4, fn = fn(x,y,z) -- Equations of the Form f1 w/ x + f2 w/ y + f3 w/ z = f4w, fn = fn(x,y,z) -- Equations of the Form f1 w/ x + f2 w/ y + f3 w/ z = f4w + f5, fn = fn(x,y,z) -- Second-Order Parabolic Equations 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 FormSecond-Order Parabolic Equations with Two Space Variables -- Heat Equation w/ t = a 2w -- Heat Equation with a Source w/ t = a 2w + (x,y,t) -- Other EquationsSecond-Order Parabolic Equations with Three or More Space Variables -- Heat Equation w/ t = a 3w -- Heat Equation with Source w/ t = a 3w + (x,y,z,t) -- Other Equations with Three Space Variables -- Equations with n Space VariablesSecond-Order Hyperbolic Equations with One Space VariableConstant Coefficient EquationsWave Equation with Axial or Central SymmetryEquations Containing Power Functions and Arbitrary ParametersEquations Containing the First Time DerivativeEquations Containing Arbitrary FunctionsSecond-Order Hyperbolic Equations with Two Space VariablesWave Equation 2w/ t2 = a2 2wNonhomogeneous Wave Equation 2w/ t2 = a2 2w + (x,y,t)Equations of the Form 2w/ t2 = a2 2w bw + (x,y,t)Telegraph Equation 2w/ t2 + k( w/ t) = a2 2w bw + (x,y,t)Other Equations with Two Space VariablesSecond-Order Hyperbolic Equations with Three or More Space VariablesWave Equation 2w/ t2 = a2 3wNonhomogeneous Wave Equation 2w/ t2 = a2 3+ (x,y,z,t)Equations of the Form 2w/ t2 = a2 3w bw + (x,y,z,t)Telegraph Equation 2w/ t2 + k( w/ t) = a2 3w bw + (x,y,z,t))Other Equations with Three Space VariablesEquations with n Space VariablesSecond-Order Elliptic Equations with Two Space VariablesLaplace Equation 2w = 0Poisson Equation 2w = (x)Helmholtz Equation 2w + w = (x)Other EquationsSecond-Order Elliptic Equations with Three or More Space VariablesLaplace Equation 3w = 0Poisson Equation 3w = (x)Helmholtz Equation 3w + w = (x)Other Equations with Three Space VariablesEquations with n Space VariablesHigher-Order Partial Differential EquationsThird-Order Partial Differential EquationsFourth-Order One-Dimensional Nonstationary EquationsTwo-Dimensional Nonstationary Fourth-Order EquationsThree- and n-Dimensional Nonstationary Fourth-Order EquationsFourth-Order Stationary EquationsHigher-Order Linear Equations with Constant CoefficientsHigher-Order Linear Equations with Variable CoefficientsSystems of Linear Partial Differential EquationsPreliminary Remarks. Some Notation and Helpful RelationsSystems of Two First-Order EquationsSystems of Two Second-Order EquationsSystems of Two Higher-Order EquationsSimplest Systems Containing Vector Functions and Operators div and curlElasticity EquationsStokes Equations for Viscous Incompressible FluidsOseen Equations for Viscous Incompressible FluidsMaxwell Equations for Viscoelastic Incompressible FluidsEquations of Viscoelastic Incompressible Fluids (General Model)Linearized Equations for Inviscid Compressible Barotropic FluidsStokes Equations for Viscous Compressible Barotropic FluidsOseen Equations for Viscous Compressible Barotropic FluidsEquations of ThermoelasticityNondissipative Thermoelasticity Equations (the Green-Naghdi Model)Viscoelasticity EquationsMaxwell Equations (Electromagnetic Field Equations)Vector Equations of General FormGeneral Systems Involving Vector and Scalar Equations: Part IGeneral Systems Involving Vector and Scalar Equations: Part IIAnalytical MethodsMethods for First-Order Linear PDEsLinear PDEs with Two Independent VariablesFirst-Order Linear PDEs with Three or More Independent VariablesSecond-Order Linear PDEs: Classification, Problems, Particular SolutionsClassification of Second-Order Linear Partial Differential EquationsBasic Problems of Mathematical PhysicsProperties and Particular Solutions of Linear EquationsSeparation of Variables and Integral Transform MethodsSeparation of Variables (Fourier Method)Integral Transform MethodCauchy Problem. Fundamental SolutionsDirac Delta Function. Fundamental SolutionsRepresentation of the Solution of the Cauchy Problem via the Fundamental SolutionBoundary Value Problems. Green's FunctionBoundary Value Problems for Parabolic Equations with One Space Variable. Green's FunctionBoundary Value Problems for Hyperbolic Equations with One Space Variable. Green's Function. Goursat ProblemBoundary Value Problems for Elliptic Equations with Two Space VariablesBoundary Value Problems with Many Space Variables. Green's FunctionConstruction of the Green's Functions. General Formulas and RelationsDuhamel's Principles. Some TransformationsDuhamel's Principles in Nonstationary ProblemsTransformations Simplifying Initial and Boundary ConditionsSystems of Linear Coupled PDEs. Decomposition MethodsAsymmetric and Symmetric DecompositionsFirst-Order Decompositions. ExamplesHigher-Order DecompositionsSome Asymptotic Results and FormulasRegular Perturbation Theory Formulas for the EigenvaluesSingular Perturbation TheoryElements of Theory of Generalized FunctionsGeneralized Functions of One VariableGeneralized Functions of Several VariablesSymbolic and Numerical Solutions with Maple, Mathematica, and MATLAB (R) Linear Partial Differential Equations with MapleIntroductionAnalytical Solutions and Their VisualizationsAnalytical Solutions of Mathematical ProblemsNumerical Solutions and Their VisualizationsLinear Partial Differential Equations with MathematicaIntroductionAnalytical Solutions and Their VisualizationsAnalytical Solutions of Mathematical ProblemsNumerical Solutions and Their VisualizationsLinear Partial Differential Equations with MATLAB (R)IntroductionNumerical Solutions of Linear PDEsConstructing Finite-Difference ApproximationsNumerical Solutions of Systems of Linear PDEsTables and SupplementsElementary Functions and Their PropertiesPower, Exponential, and Logarithmic FunctionsTrigonometric FunctionsInverse Trigonometric FunctionsHyperbolic FunctionsInverse Hyperbolic FunctionsFinite Sums and Infinite SeriesFinite Numerical SumsFinite Functional SumsInfinite Numerical SeriesInfinite Functional SeriesIndefinite and Definite IntegralsIndefinite IntegralsDefinite IntegralsIntegral TransformsTables of Laplace TransformsTables of Inverse Laplace TransformsTables of Fourier Cosine TransformsTables of Fourier Sine TransformsCurvilinear Coordinates, Vectors, Operators, and Differential RelationsArbitrary Curvilinear Coordinate SystemsCartesian, Cylindrical, and Spherical Coordinate SystemsOther Special Orthogonal CoordinatesSpecial Functions and Their PropertiesSome Coefficients, Symbols, and NumbersError Functions. Exponential and Logarithmic IntegralsSine Integral and Cosine Integral. Fresnel IntegralsGamma Function, Psi Function, and Beta FunctionIncomplete Gamma and Beta FunctionsBessel Functions (Cylindrical Functions)Modified Bessel FunctionsAiry FunctionsDegenerate Hypergeometric Functions (Kummer Functions)Hypergeometric FunctionsLegendre Polynomials, Legendre Functions, and Associated Legendre FunctionsParabolic Cylinder FunctionsElliptic IntegralsElliptic FunctionsJacobi Theta FunctionsMathieu Functions and Modified Mathieu FunctionsOrthogonal PolynomialsNonorthogonal PolynomialsReferencesIndex
Includes nearly 4,000 linear partial differential equations (PDEs) with solutions. Presents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fields. Outlines basic methods for solving various problems in science and engineering. Contains much more linear equations, problems, and solutions than any other book currently available. Provides a database of test problems for numerical and approximate analytical methods for solving linear PDEs and systems of coupled PDEs. New to the Second Edition: More than 700 pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutions -- Systems of coupled PDEs with solutions -- Some analytical methods, including decomposition methods and their applications -- Symbolic and numerical methods for solving linear PDEs with Maple, Mathematica, and MATLAB -- Many new problems, illustrative examples, tables, and figures. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity.