Applied Functional Analysis

The area of functional analysis plays a central role in the technical sciences as the fundamental framework for modelling and analysis for a broad range of problems in classical disciplines and newer areas of inter-disciplinary nature. The methods of functional analysis have helped solve diverse real-world problems in optimisation, modelling, analysis, numerical approximation and computer simulation. With a comprehensive presentation of functional analysis results surfacing repeatedly in scientific and technological applications, this book expertly presides over the most current analytical and numerical methods in infinite-dimensional spaces. It introduces recent results in wavelet and Gabor analysis as applied in partial differential equations and signal and image processing. The main objective of this book is to present all those results of functional analysis which have been frequently applied in emerging areas of science and technology. The book is self-contained and provides examples, updated references and application in diverse fields. The set problems are thought provoking and many lead to new results and applications. The book is intended to be a textbook for senior undergraduate and graduate students in mathematics. It will also be useful for an advanced course in systems engineering, computer engineering and management sciences. Contents: 1. Metric Spaces and Banach Fixed Point Theorem 2. Banach Spaces 3. Hilbert Space 4. Fundamental Theorems 5. Differential and Integral Calculus in Banach Spaces 6. Optimisation Problems 7. Operator Equations and Variational Methods 8. Finite Element and Boundary Element Methods 9. Variational Inequalities and Applications 10. Spectral Theory with Application 11. Frame and Basis Theory in Hilbert Spaces 12. Wavelet Theory 13. Wavelet Method for Partial Differential Equations and Image Processing 14. Wavelet Frames 15. Gabor AnalysisAlso available: INTRODUCTION TO WAVELET ANALYSIS WITH APPLICATIONS - ISBN 1848290276 Solar Distillation Practice For Water Desalination Systems - ISBN 1905740883Anshan Publishers is a publisher of fine medical, scientific, and technical books. We find the best titles from our worldwide publishing partners and bring them to the global marketplace. We publish in a wide range of fields, including:- Biological Sciences Biotechnology Chemistry Engineering Material Science Microbiology Pure and Applied Physics Pure and Applied Mathematics Statistics