http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
with applications to boundary value problems and finite elements
1 online resource (xiv, 471 pages) : illustrations.
THIS IS BOTH PROMO COPY AND BACK COVER COPY!!!!! This book provides an introduction to functional analysis and treats in detail its application to boundary-value problems and finite elements. The book is intended for use by senior undergraduate and graduate students in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis would also find the text useful. The text is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. Readers of this book can expect to obtain a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.
Part I. Linear functional analysis -- 1. Sets -- 2. Sets of functions and Lebesgue integration -- 3. Vector spaces, normed, and inner product spaces -- 4. Properties of normed spaces -- 5. Linear operators -- 6. Orthonormal bases and Fourier series -- 7. Distributions and Sobolev spaces -- Part II. Elliptic boundary value problems -- 8. Elliptic boundary value problems -- 9. Variational boundary value problems -- 10. Approximate methods of solution -- Part III. The finite element method -- 11. The finite element method -- 12. Analysis of the finite element method.
Includes bibliographical references (pages [435]-439) and index.