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.
ordinary differential equations
classical theory of partial differential equations
Laplace and Poisson equations
variational methods of solution of corresponding boundary value problems
methods of solution for evolution partial differential equations
The 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.
Table of Contents
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
"Numerous technical and physical examples explained in a very clear manner help to understand better theoretical material and motivate further exploration of the subject. Accumulating many years of the author's teaching experience at the Technical University of Prague, this excellent book will be of benefit for engineers, scientists, and mathematicians dealing with boundary value problems, as well as students of science and engineering."
-Yuri V. Rogovchenko (Famagusta), Zentralblatt Math, Vol. 1078, April 2006
"A very nice text...addressed to the non-mathematician."
- Ivo Babuska, Professor of Engineering and Mathematics, University of Texas
"This book is unusual in that it sits at the intersection of differential equations and numerical analysis, and in this regard it represents a modern approach to the subject. A good discussion…"
-CHOICE, May 1999