Handbook of Linear Partial Differential Equations for Engineers and Scientists

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, 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.

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.