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

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Book Preface

The Handbook of Linear Partial Differential Equations for Engineers and Scientists, a unique reference for scientists and engineers, contains nearly 4,000 linear partial differential equations with solutions as well as analytical, symbolic, and numerical methods for solving linear equations. First-, second-, third-, fourth-, 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 partial differential equations 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 second edition has been substantially updated, revised, and expanded. More than 1,500 linear equations and systems with solutions, as well some methods and many examples, have been added, which amounts to over 700 pages of new material (including 250 new pages dealing with methods).

New to the second edition:

• Some second-, third-, fourth-, and higher-order linear PDEs with solutions.
• Systems of coupled partial differential equations with solutions.
• First-order linear PDEs with solutions.
• Some analytical methods including decomposition methods and their applications.
• Symbolic and numerical methods with Maple, Mathematica, and MATLAB.
• Some transformations, asymptotic formulas and solutions.
• Many new examples and figures included for illustrative purposes.
• Some long tables, including tables of various integral transforms.