Handbook of First Order Partial Differential Equations by Andrei D. Polyanin, Valentin F. Zaitsev, Alain Moussiaux
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About this book :-
Handbook of First Order Partial Differential Equations written by
Andrei D. Polyanin, Valentin F. Zaitsev, Alain Moussiaux
First order partial differential equations are encountered in various fields of science and numerous applications (differential geometry, analytical mechanics, solid mechanics, gas dynamics, geometric optics, wave theory, heat and mass transfer, multi phase flows, control theory, differential games, calculus of variations, dynamic programming, chemical engineering sciences, etc.).
The book contains about 3000 first order partial differential equations with solutions. Many new exact solutions to linear and nonlinear equations are included (a large portion of these solutions was constructed by "recalculating" the corresponding results obtained by the authors over the last decade in the field of ordinary differential equations). Special attention is paid to equations of general form which depend on arbitrary functions. Other equations contain one or more free parameters (lhe book actually deals with families of differential equations); it is the reader's option to fix these parameters. A number of differential equations are considered which are encountered in various fields of applied mathematics, mechanics, physics, control theory, and engineering sciences. Totally, the number of equations described is several times greater than in any other book available. The handbook consists of chapters, sections, and subsections. The equations within a subsection are arranged in the increasing order of complexity. An extensive table of contents provides rapid access to the desired equations.
The authors hope that the handbook will prove helpful for a wide readership of researchers, college and university teachers, engineers, and students in various fields of applied mathematics, mechanics, physics, optimal control, differential garnes, and engineering sciences.
(Andrei D. Polyanill, Valentin F. Zaitsev, Alain Moussiat)
Book Detail :-
Title: Handbook of First Order Partial Differential Equations
Edition:
Author(s): Andrei D. Polyanin, Valentin F. Zaitsev, Alain Moussiaux
Publisher: CRC Press
Series: Differential and Integral Equations and Their Applications
Year: 2001
Pages: 515
Type: PDF
Language: English
ISBN: 041527267X,9780415272674
Country: Rassia
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About Author :-
The author 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 Valentin F. Zaitsev , Ph.D., D.Se., is a noted scientist in the fields of ordinary differential equations, mathematical physics, and nonlinear mechanics.
Valentin Zaitsev graduated from the Radio Electronics Faculty of the Leningrad Poly technical Institute (now Saint-Petersburg Technical University) in 1969 and received his Ph.D. degree in 1983 at the Leningrad State University. His Ph.D. thesis was devoted to the group approach to the study of some classes of ordinary differential equations. In 1992, Professor Zaitsev received his Doctor of Sciences degree; his D.Sc. thesis was dedicated to the discrete-group analysis of ordinary differential equations.
In 1971-1996, Valentin Zaitsev worked in the Research Institute for Computational Mathematics and Control Processes of the SL Petersburg State University. Since 1996. Professor Zaitsev has been a member of the staff of the Russian State Pedagogical University.
Professor Zaitsev has made important contributions to new methods in the theory of ordinary and partial differential equations. He is an author of more than 110 scientific publications. including 15 books and one patent. E-mail: z:[email protected]
AJain Moussiaux, Ph.D., D.Se., is a prominent scientist in the fields of computer algebra, general relativity models. and differential equations.
Alain Moussiaux was born in 1943 in Belgium. He graduated from the University of Liege as a physicist in 1965 and received his Ph.D. degree in 1972 at the University of Namm (Belgium). His thesis was devoted to the application of the Riemann method for sLUdying progressive waves in various star models. Since 1968.
Doctor Moussiaux has been a member of the staff of the Physical Department at the University of Namur. Alain Moussiaux came to computer algebra from general relativity models and mathematical physics models. One of his most significant achievements is the development of the CONVODE a software for analytical solution of ordinary and partial differentia] equations.
Doctor Moussiaux is an author of various books and publications in the fields of computer algebra, mathematical physics, and general relativity models. In 1982, Alain Moussiaux became a laureate of the Belgium Academy of Sciences for his work in computer algebra. E-mail: [email protected]
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Book Contents :-
Handbook of First Order Partial Differential Equations written by
Andrei D. Polyanin, Valentin F. Zaitsev, Alain Moussiaux
cover the following topics.
Preface
Authors
Contents
Annotation
Some Notation And Remarks
Part I. Linear Equations With Two Independent Variables
1. Equations Containing One Derivative
2. Linear Equations of the Form f(x, y) ~: + g(x,y) ~~ = 0
3. LinearEquationsoftheFormf(x,y)~-:: +g(x,y)~; =h(x,y)
4. LinearEquationsoftheFormf(x,y)~,: +g(x,y)~~ =h(x,y)w
5. LinearEquationsoftheFormf(x,y)~,: +g(x,y)~~ =ht(x,y)w+ho(x,y)
Part II. Linear Equations With Three or More Independent Variables
6. Linear Equations of the Form I(x, y, z} ~
: + g(x, y, z) ~~ + hex, y, z)
7. Linear Equations of the Form It ~= + 12 ~~ + 13 ~
: = 14, In = In{x,y, z)
8. Linear Equations of the Form il ~~ + i2 ~; + i3 ~~ = f4W, in = fn(x, y, z)
9. Linear Equations of the Form it ~: +!2 ~~ + i3 ~
; = !4W + is, in = in(x, y, z)
10. Linear Equations With Four or More Independent Variables
Part III. Nonlinear Equations
11. Quasilinear Equations of the Form f(x, y) 88w + g(x, y) 8aW = hex, y, w)
12. Quasilinear Equations of the Form f(x, y, w) ~~ + g(x, y, w) ~~ = hex, y, w)
13. Equations With 1\vo Independent Variables Quadratic in Derivatives
14. Nonlinear Equations With Two Independent Variables of General Form
15. Nonlinear Equations With Three or More Independent Variables
Supplement. Solution of Differential Equations Through the CONVODE Software
S.l.Introduction
S.2. Examples of Solving Ordinary Differential Equations
S.3. Examples of Solving Partial Differential Equations
SA. How to Use CONVODE
References
Index
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