# Handbook of Linear Partial Differential Equations for Engineers and Scientists: Second Edition

*Andrei D. Polyanin, Vladimir E. Nazaikinskii*

*The Handbook of Linear Partial Differential Equations for Engineers and Scientists*, a unique reference for scientists and engineers, contains nearly 4,000 linear PDEs with solutions as well as analytical, symbolic, and numerical methods for solving linear equations. 1st-, 2nd-, 3rd-, 4th-, and higher-order linear equations and systems of coupled equations are considered. Equations of parabolic, hyperbolic, elliptic, mixed, and other types are discussed. A number of new linear equations, exact solutions, transformations, and methods are described. Formulas for effective construction of solutions are given. A number of specific examples where the methods described in the book are used are considered. Boundary value problems and eigenvalue problems are described. Symbolic and numerical methods for solving PDEs with Maple, Mathematica, and MATLAB R are considered. All in all, the handbook contains many more linear PDEs than any other book currently available.

In selecting the material, the authors have given highest priority to the following major topics:

• Equations and problems that arise in various applications (heat and mass transfer theory, wave theory, elasticity, hydrodynamics, aerodynamics, continuum mechanics, acoustics, electrostatics, electrodynamics, electrical engineering, diffraction theory, quantum mechanics, chemical engineering sciences, control theory, etc.).

• Systems of coupled equations that arise in various fields of continuum mechanics and physics.

• Analytical and symbolic methods for solving linear equations of mathematical physics.

• Equations of general form that depend on arbitrary functions and equations that involve many free parameters; exact solutions of such equations are of major importance for testing numerical and approximate analytical methods.

The 2e is greatly updated, revised, and expanded.