Handbook of Linear Partial Differential Equations for Engineers and Scientists (2E) by Andrei D. Polyanin, Vladimir E. Nazaikinskii
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About this book :-
Handbook of Linear Partial Differential Equations for Engineers and Scientists (2E) written by
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 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.
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.
• 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.
• Extensive table of contents and detailed index.
(Andrei D. Polyanin)
Book Detail :-
Title: Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems
Edition: 2nd
Author(s): Andrei D. Polyanin, Vladimir E. Nazaikinskii
Publisher: Chapman and Hall/CRC
Series:
Year: 2016
Pages: 1623
Type: PDF
Language: English
ISBN: 146658145X,9781466581456
Country: Russia
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About Author :-
The author Andrei D. Polyanin Andrei D. Polyanin, D.Se., Ph.D., is a noted scientist of broad interests (ordinary differential, partial differential, and integral equations, mathematical physics, engineering mathematics, nonlinear mechanics, heat and mass transfer. chemical hydrodynamics, and others).
Andrei Polyanin graduated from the Department of Mechanics and Mathematics of the Moscow State University in 1974. He received his Ph.D. degree in 1981 and D.Se. degree in 1986 at the Institute for Problems in Mechanics of the Russian (former USSR) Academy of Sciences. Since 1975, Andrei Polyanin has been a member of the staff of the Institute for Problems in Mechanics of the Russian Academy of Sciences.
Professor Polyanin is an author of 21 books in English. Russian, German, and Bulgarian. His publications also include more than 120 research papers and three patents. In 1991, Andrei Polyanin was awarded a Chaplygin Prize of the USSR Academy of Sciences for his research in mechanics. E-mail: [email protected]
The author Vladimir E. Nazaikinskii , D.Sc., is an actively working mathematician specializing in partial differential equations, mathematical physics, and noncommutative analysis. He was born in 1955 in Moscow, graduated from the Moscow Institute of Electronic Engineering in 1977, defended his Ph.D. in 1980 and D.Sc. in 2014, and worked at the Institute for Automated Control Systems, Moscow Institute of Electronic Engineering, Potsdam University, and Moscow State University. Currently he is a senior researcher at the Institute for Problems in Mechanics, Russian Academy of Sciences. He is the author of seven monographs and more than 90 papers on various aspects of noncommutative analysis, asymptotic problems, and elliptic theory.
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Book Contents :-
Handbook of Linear Partial Differential Equations for Engineers and Scientists (2E) written by
Andrei D. Polyanin, Vladimir E. Nazaikinskii
cover the following topics.
Part I Exact Solutions
1. First-Order Equations with Two Independent Variables Independent Variables
2. First-Order Equations with Three or More Independent Variables
3. Second-Order Parabolic Equations with One Space Variable
4. Second-Order Parabolic Equations with Two Space Variables
5. Second-Order Parabolic Equations with Three or More Space Variables
6. Second-Order Hyperbolic Equations with One Space Variable
7. Second-Order Hyperbolic Equations with Two Space Variables
8. Second-Order Hyperbolic Equations with Three or More Space Variables
9. Second-Order Elliptic Equations with Two Space Variables
10. Second-Order Elliptic Equations with Three or More Space Variables
11. Higher-Order Partial Differential Equations
12. Systems of Linear Partial Differential Equations
Part II Analytical Methods
13. Methods for First-Order Linear PDEs
14. Second-Order Linear PDEs: Classification, Problems, Particular Solutions
15. Separation of Variables and Integral Transform Methods
16. Cauchy Problem. Fundamental Solutions
17. Boundary Value Problems. Green’s Function
18. Duhamel’s Principles. Some Transformations
19. Systems of Linear Coupled PDEs. Decomposition Methods
20. Some Asymptotic Results and Formulas
21. Elements of Theory of Generalized Functions
22. Linear Partial Differential Equations with Maple
23. Linear Partial Differential Equations with Mathematica
24. Linear Partial Differential Equations with MATLAB R
Part IV Tables and Supplements
25. Elementary Functions and Their Properties
26. Finite Sums and Infinite Series
27. Indefinite and Definite Integrals
28. Integral Transforms
29. Curvilinear Coordinates, Vectors, Operators, and Differential Relations
30. Special Functions and Their Properties
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