Bøger af Andrei D. Polyanin

Delay Ordinary and Partial Differential Equations is intended for a broad audience of scientists, university professors, and graduate and postgraduate students specializing in applied and computational mathematics, mathematical physics, mechanics, control theory, biology, medicine, chemical technology, ecology, and economics.

The book is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear PDEs. It also presents the direct method of symmetry reductions and its more general version.

A systematic exposition of fundamental problems of hydrodynamics, heat and mass transfer, and physicochemical hydrodynamics, which constitute the theoretical basis of chemical engineering in science. Topics are arranged in increasing order of difficulty, beginning with a physical and mathematical statement of the problem, followed by final results.

With numerous examples, this handbook takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that frequently occur in scientific, engineering applications and education. The book addresses difficult issues that many engineers and students face and avoids special terminology whenever possible.

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.

A reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences, this title contains about 3000 first order partial differential equations with solutions.