Andrei D. Polyanin, Vladimir E. Nazaikinskii

Handbook of Linear Partial Differential Equations for Engineers and Scientists (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This second edition contains nearly 4,000 linear partial differential equations (PDEs) 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, mixed, and other types are discussed. New linear equations, exact solutions, transformations, and methods are described. Formulas for effective construction of solutions are given. Boundary value and eigenvalue problems are addressed. Symbolic and numerical methods for solving PDEs with Maple, Mathematica, and MATLAB are explored.

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Produktdetails

• Verlag: Taylor & Francis
• Erscheinungstermin: 23. Dezember 2015
• Englisch
• ISBN-13: 9781040074077
• Artikelnr.: 72273087

Autorenporträt

Andrei D. Polyanin, D.Sc., is an internationally renowned scientist of broad interests and is active in various areas of mathematics, mechanics, and chemical engineering sciences. He is one of the most prominent authors in the field of reference literature on mathematics. Professor Polyanin graduated with honors from the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University in 1974. He received his Ph.D. in 1981 and D.Sc. in 1986 at the Institute for Problems in Mechanics of the Russian Academy of Sciences. Since 1975, Professor Polyanin has been working at the Institute for Problems in Mechanics of the Russian Academy of Sciences. He is also professor of applied mathematics at Bauman Moscow State Technical University and at National Research Nuclear University MEPhI. He is a member of the Russian National Committee on Theoretical and Applied Mechanics and the Mathematics and Mechanics Expert Council of the Higher Certification Committee of the Russian Federation. Professor Polyanin has authored more than 30 books in English, Russian, German, and Bulgarian as well as more than 170 research papers, three patents, and a number of fundamental handbooks. Professor Polyanin is editor-in-chief of the website EqWorld-The World of Mathematical Equations, editor of the book series Differential and Integral Equations and Their Applications, and a member of the editorial board of the journals Theoretical Foundations of Chemical Engineering, Mathematical Modeling and Computational Methods, and Bulletin of the National Research Nuclear University MEPhI. In 1991, Professor Polyanin was awarded the Chaplygin Prize of the Russian Academy of Sciences for his research in mechanics. In 2001, he received an award from the Ministry of Education of the Russian Federation.

Vladimir E. Nazaikinskii, D.Sc., is an actively working mathematician specializing in partial differential equations, m

Inhaltsangabe

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.