Handbook of Linear Partial Differential Equations for Engineers and Scientists

ISBN-13: 9781466581456 / Angielski / Twarda / 2016 / 1609 str.

Andrei D. Polyanin; Vladimir E. Nazaikinskii

Opis

• 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^(r)
• 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.

Spis treści

Exact Solutions. First-Order Equations with Two Independent Variables. First-Order Equations with Three or More Independent Variables. Second-Order Parabolic Equations with One Space Variable. Second-Order Parabolic Equations with Two Space Variables. Second-Order Parabolic Equations with Three or More Space Variables. Second-Order Hyperbolic Equations with One Space Variable. Second-Order Hyperbolic Equations with Two Space Variables. Second-Order Hyperbolic Equations with Three or More Space Variables. Second-Order Elliptic Equations with Two Space Variables. Second-Order Elliptic Equations with Three or More Space Variables. Higher-Order Partial Differential Equations. Systems of Linear Partial Differential Equations. Analytical Methods. Methods for First-Order Linear PDEs. Second-Order Linear PDEs: Classification, Problems, Particular Solutions. Separation of Variables and Integral Transform Methods. Cauchy Problem. Fundamental Solutions.
Boundary Value Problems. Green’s Function. Duhamel’s Principles. Some Transformations. Systems of Linear Coupled PDEs. Decomposition Methods. Some Asymptotic Results and Formulas. Elements of Theory of Generalized Functions. Symbolic and Numerical Solutions with Maple, Mathematica, and MATLAB^®. Linear Partial Differential Equations with Maple. Linear Partial Differential Equations with Mathematica. Linear Partial Differential Equations with MATLAB^®. Tables and Supplements. Elementary Functions and Their Properties. Finite Sums and Infinite Series. Indefinite and Definite Integrals. Integral Transforms. Curvilinear Coordinates, Vectors, Operators, and Differential Relations. Special Functions and Their Properties.