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 = h 1( x,y ) w + h 0( 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 f 1 ∂w/∂x + f 2 ∂w/∂y + f 3 ∂w/∂z = f 4 , fn= fn ( x,y,z ) Equations of the Form f 1 ∂w/∂x + f 2 ∂w/∂y + f 3 ∂w/∂z = f 4 w, fn= fn ( x,y,z ) Equations of the Form f 1 ∂w/∂x + f 2 ∂w/∂y + f 3 ∂w/∂z = f 4 w + f 5 , 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 Form Second-Order Parabolic Equations with Two Space Variables Heat Equation ∂w/∂t = a'^+2w Heat Equation with a Source ∂w/∂t = a'^+2w + Õ"( x,y,t ) Other Equations Second-Order Parabolic Equations with Three or More Space Variables Heat Equation ∂w/∂t = a'^+3w Heat Equation with Source ∂w/∂t = a'^+3w + Õ"( x,y,z,t ) Other Equations with Three Space Variables Equations with n Space Variables Second-Order 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 Second-Order Hyperbolic Equations with Two Space Variables Wave Equation ∂2w/∂t2= a2'^+2w Nonhomogeneous Wave Equation ∂2w/∂t2= a2'^+2w + Õ"( x,y,t ) Equations of the Form ∂2w/∂t2= a2'^+2w − bw + Õ"( x,y,t ) Telegraph Equation ∂2w/∂t2+ k(∂w/∂t) = a2'^+2w − bw + Õ"( x,y,t ) Other Equations with Two Space Variables Second-Order Hyperbolic Equations with Three or More Space Variables Wave Equation ∂2w/∂t2= a2'^+3w Nonhomogeneous Wave Equation ∂2w/∂t2= a2'^+3+ Õ"( x,y,z,t )Equations of the Form ∂2w/∂t2= a2'^+3w − bw + Õ"( x,y,z,t ) Telegraph Equation ∂2w/∂t2+ k(∂w/∂t) = a2'^+3w − bw + Õ"( x,y,z,t ) ) Other Equations with Three Space Variables Equations with n Space Variables Second-Order Elliptic Equations with Two Space Variables Laplace Equation '^+2w = 0 Poisson Equation '^+2w = − Õ"( x ) Helmholtz Equation '^+2w + λw = − Õ"( x ) Other Equations Second-Order Elliptic Equations with Three or More Space Variables Laplace Equation '^+3w = 0 Poisson Equation '^+3w = − Õ"( x ) Helmholtz Equation '^+3w + λw = − Õ"( x ) Other Equations with Three Space Variables 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 Three- and n -Dimensional Nonstationary Fourth-Order Equations Fourth-Order Stationary Equations Higher-Order Linear Equations with Constant Coefficients Higher-Order Linear Equations with Variable Coefficients Systems of Linear Partial Differential Equations Preliminary Remarks. Some Notation and Helpful Relations Systems of Two First-Order Equations Systems of Two Second-Order Equations Systems of Two Higher-Order Equations Simplest Systems Containing Vector Functions and Operators div and curl Elasticity Equations Stokes Equations for Viscous Incompressible Fluids Oseen Equations for Viscous Incompressible Fluids Maxwell Equations for Viscoelastic Incompressible Fluids Equations of Viscoelastic Incompressible Fluids (General Model) Linearized Equations for Inviscid Compressible Barotropic Fluids Stokes Equations for Viscous Compressible Barotropic Fluids Oseen Equations for Viscous Compressible Barotropic Fluids Equations of Thermoelasticity Nondissipative Thermoelasticity Equations (the Green-Naghdi Model) Viscoelasticity Equations Maxwell Equations (Electromagnetic Field Equations) Vector Equations of General Form General Systems Involving Vector and Scalar Equations: Part I General Systems Involving Vector and Scalar Equations: Part II Analytical Methods Methods for First-Order Linear PDEs Linear PDEs with Two Independent Variables First-Order Linear PDEs with Three or More Independent Variables Second-Order Linear PDEs: Classification, Problems, Particular Solutions Classification of Second-Order Linear Partial Differential Equations Basic Problems of Mathematical Physics Properties and Particular Solutions of Linear Equations Separation of Variables and Integral Transform Methods Separation of Variables (Fourier Method) Integral Transform Method Cauchy Problem. Fundamental Solutions Dirac Delta Function. Fundamental Solutions Representation of the Solution of the Cauchy Problem via the Fundamental Solution Boundary Value Problems. Green''s Function Boundary Value Problems for Parabolic Equations with One Space Variable. Green''s Function Boundary Value Problems for Hyperbolic Equations with One Space Variable. Green''s Function. Goursat Problem Boundary Value Problems for Elliptic Equations with Two Space Variables Boundary Value Problems with Many Space Variables.

Green''s Function Construction of the Green''s Functions. General Formulas and Relations Duhamel''s Principles. Some Transformations Duhamel''s Principles in Nonstationary Problems Transformations Simplifying Initial and Boundary Conditions Systems of Linear Coupled PDEs. Decomposition Methods Asymmetric and Symmetric Decompositions First-Order Decompositions. Examples Higher-Order Decompositions Some Asymptotic Results and Formulas Regular Perturbation Theory Formulas for the Eigenvalues Singular Perturbation Theory Elements of Theory of Generalized Functions Generalized Functions of One Variable Generalized Functions of Several Variables Symbolic and Numerical Solutions with Maple, Mathematica, and MATLAB® Linear Partial Differential Equations with Maple Introduction Analytical Solutions and Their Visualizations Analytical Solutions of Mathematical Problems Numerical Solutions and Their Visualizations Linear Partial Differential Equations with Mathematica Introduction Analytical Solutions and Their Visualizations Analytical Solutions of Mathematical Problems Numerical Solutions and Their Visualizations Linear Partial Differential Equations with MATLAB® Introduction Numerical Solutions of Linear PDEs Constructing Finite-Difference Approximations Numerical Solutions of Systems of Linear PDEs Tables and Supplements Elementary Functions and Their Properties Power, Exponential, and Logarithmic Functions Trigonometric Functions Inverse Trigonometric Functions Hyperbolic Functions Inverse Hyperbolic Functions Finite Sums and Infinite Series Finite Numerical Sums Finite Functional Sums Infinite Numerical Series Infinite Functional Series Indefinite and Definite Integrals Indefinite Integrals Definite Integrals Integral Transforms Tables of Laplace Transforms Tables of Inverse.