Applied Functional Analysis, Second Edition

Published:
Author(s):
Request
Evaluation Copy

Purchasing Options

Hardback
Not available
in your region
ISBN 9780849325519
Cat# 2551
 

Features

  • Provides a complete study of functional analysis, starting with elementary mathematics
  • Offers a consistent and logical development of advanced topics
  • Gives extensive examples, providing motivation for studying abstract notions
  • Illustrated to aid development of intuition and understanding
  • Includes advanced topics, particularly, Hilbert spaces, an introduction to the spectral theory of linear operators, and applications to boundary-value problems of partial differential equations of mathematical physicsMarketing Class Code: 3NO5 (Physical Science/Mathematics/Computational Mathematics)
  • Summary

    Functional analysis-the study of the properties of mathematical functions-is widely used in modern scientific and engineering disciplines, particularly in mathematical modeling and computer simulation. Applied Functional Analysis, the only textbook of its kind, is designed specifically for the graduate student in engineering and science who has little or no training in advanced mathematics. Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophisticated functional analysis. This self-contained presentation requires few mathematical prerequisites and provides students with the fundamental concepts and theorems essential to mathematical analysis and modeling.
    Applied Functional Analysis combines various principles of mathematics, computer science, engineering, and science, laying the foundation for further specialty work in partial differential equations, approximation theory, numerical mathematics, control theory, mathematical physics, and related subjects. This new treatment of a classic subject outfits engineering and science majors with a graduate-level mathematics standing, otherwise accessible only through regular mathematics studies.

    Table of Contents

    Preliminaries
    Elementary Set Theory
    Elementary Logic
    Relations
    Functions
    Cardinality of Sets
    Foundations of Abstract Algebra
    Elementary Topology in Rn
    Elements of Differential and Integral Calculus
    Linear Algebra
    Vector Spaces - The Basic Concepts
    Linear Transformations
    Algebraic Duals
    Euclidean Spaces
    Lebesgue Measure and Integration
    Lebesgue Measure
    Lebesgue Integration Theory
    Lp-Spaces
    Topological and Metric Spaces
    Elementary Topology
    Theory of Metric Spaces
    Banach Spaces
    Topological Vector Spaces
    Hahn-Banach Extension Theorem
    Bounded (Continuous) Linear Operators on Normed Spaces
    Closed Operators
    Topological Duals: Weak Compactness
    Closed Range Theorem: Solvability of Linear Equations
    Hilbert Spaces
    Basic Theory
    Duality in Hilbert Spaces
    Elements of Spectral Theory
    References
    Index

    Related Titles