Characteristic Features
• Includes nearly 4,000 linear partial differential equations (PDEs) with solutions
• Presents solutions to 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 analytical methods for solving various problems in science and engineering
• Contains many more linear PDEs, problems, solutions, and transformations 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 Third Edition
• Chapter on linear ODEs and PDEs with delays
• Chapter on linear ODEs and PDEs with fractional derivatives
• Some individual PDEs, solutions, transformations, formulas, and problems
• Two sections on special functions used to solve linear ODEs and PDEs with delay or fractional derivatives.
To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, and they outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity.
Table of Contents:
Part 1: Exact Solutions 1. Second-Order Parabolic Equations with One Space Variable 2. Second-Order Parabolic Equations with Two Space Variables 3. Second-Order Parabolic Equations with Three or More Space Variables 4. Second-Order Hyperbolic Equations with One Space Variable 5. Second-Order Hyperbolic Equations with Two Space Variable 6. Second-Order Hyperbolic Equations with Three or More Space Variables 7. Second-Order Elliptic Equations with Two Space Variables 8. Second-Order Elliptic Equations with Three or More Space Variables 9. Higher-Order Partial Differential Equations 10. Systems of Linear Partial Differential Equations Part 2: Analytical Methods 11. Methods for First-Order Linear PDEs 12. Second-Order Linear PDEs: Classification, Problems, Particular Solutions 13. Separation of Variables and Integral Transform Methods 14. Cauchy Problem: Fundamental Solutions 15. Boundary Value Problems: Green’s Function 16. Duhamel’s Principles: Some Transformations 17. Systems of Linear Coupled PDEs: Decomposition Methods 18. Some Asymptotic Results and Formulas 19. Linear Partial Differential Equations with Delay 20. Linear Fractional Partial Differential Equations 21. Elements of Theory of Generalized Functions Part 3: Tables and Supplements 22. Indefinite and Definite Integrals 23. Integral Transforms 24. Curvilinear Coordinates, Vectors, Operators, and Differential Relations 25. Some Special Functions and Their Properties
About the Author :
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 300 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, 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 150 papers on various aspects of noncommutative analysis, asymptotic problems, and elliptic theory.
