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Analysis for Applied Mathematics

ISBN-10: 0387952799
ISBN-13: 9780387952796
Edition: 2001
Authors: Ward Cheney
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Description: The author describes this marvelous book as designed for beginning graduate students in mathematics-in particular for those who intend to specialize in applied mathematics, and for graduate students in other disciplines such as engineering, physics  More...

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Book details

Copyright year: 2001
Publisher: Springer
Publication date: 6/21/2001
Binding: Hardcover
Pages: 448
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.694
Language: English

The author describes this marvelous book as designed for beginning graduate students in mathematics-in particular for those who intend to specialize in applied mathematics, and for graduate students in other disciplines such as engineering, physics and computer science. The first six chapters contain enough material for a year course, and the final two chapters contain related material Those who are familiar with the authors earlier books will not be surprised by its excellence. It is businesslike and will be found to be demanding, but it is user-friendly. It is the reviewers opinion that it will be extremely useful and popular as a text; institutions that do not already require their students to take such a course no longer have an excuse, and should immediately organize one based on this book. Mathematical Reviews

Preface
Normed Linear Spaces
Definitions and Examples
Convexity, Convergence, Compactness, Completeness
Continuity, Open Sets, Closed Sets
More About Compactness
Linear Transformations
Zorn's Lemma, Hamel Bases, and the Hahn-Banach Theorem
The Baire Theorem and Uniform Boundedness
The Interior Mapping and Closed Mapping Theorems
Weak Convergence
Reflexive Spaces
Hilbert Spaces
Geometry
Orthogonality and Bases
Linear Functionals and Operators
Spectral Theory
Sturm-Liouville Theory
Calculus in Banach Spaces
The Frechet Derivative
The Chain Rule and Mean Value Theorems
Newton's Method
Implicit Function Theorems
Extremum Problems and Lagrange Multipliers
The Calculus of Variations
Basic Approximate Methods of Analysis
Discretization
The Method of Iteration
Methods Based on the Neumann Series
Projections and Projection Methods
The Galerkin Method
The Rayleigh-Ritz Method
Collocation Methods
Descent Methods
Conjugate Direction Methods
Methods Based on Homotopy and Continuation
Distributions
Definitions and Examples
Derivatives of Distributions
Convergence of Distributions
Multiplication of Distributions by Functions
Convolutions
Differential Operators
Distributions with Compact Support
The Fourier Transform
Definitions and Basic Properties
The Schwartz Space
The Inversion Theorems
The Plancherel Theorem
Applications of the Fourier Transform
Applications to Partial Differential Equations
Tempered Distributions
Sobolev Spaces
Additional Topics
Fixed-Point Theorems
Selection Theorems
Separation Theorems
The Arzela-Ascoli Theorems
Compact Operators and the Fredholm Theory
Topological Spaces
Linear Topological Spaces
Analytic Pitfalls
Measure and Integration
Extended Reals, Outer Measures, Measurable Spaces
Measures and Measure Spaces
Lebesgue Measure
Measurable Functions
The Integral for Nonnegative Functions
The Integral, Continued
The L[superscript p]-Spaces
The Radon-Nikodym Theorem
Signed Measures
Product Measures and Fubini's Theorem
References
Index
Symbols

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