Solving Ordinary and Partial Boundary Value Problems in Science and Engineering

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This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: - ordinary differential equations - classical theory of partial differential equations- Laplace and Poisson equations - heat equation - variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equationsThe author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction. TOC:Ordinary Differential Partial Equations with Boundary Conditions.- Eigenvalue Problems.- Partial Differential Equations.- Classical Approach.- Variational Methods of Solutions of Elliptic Boundary Value Problems.- Generalized Solutions and Their Approximations.- Weak Solutions.- The Finite-Difference Method for Partial Differential Equations.- The Method of Discretization in Time (the Rothe Method).- The Fourier Method.