UID:
almahu_9947367642002882
Format:
1 online resource (442 p.)
Edition:
2nd ed. / Vivian Hutson, John S. Pym, Michael J. Cloud.
ISBN:
1-281-01911-9
,
9786611019112
,
0-08-052731-0
Series Statement:
Mathematics in science and engineering, v. 200
Content:
Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Key Features- Provides an ideal transition between introductory math courses and advanced graduate study in applied math
Note:
Description based upon print version of record.
,
Cover; Copyright Page; Preface; Acknowledgements; Contents; Chapter 1. Banach Spaces; 1.1 Introduction; 1.2 Vector Spaces; 1.3 Normed Vector Spaces; 1.4 Banach Spaces; 1.5 Hilbert Space; Problems; Chapter 2. Lebesgue Integration and the Lp Spaces; 2.1 Introduction; 2.2 The Measure of a Set; 2.3 Measurable Functions; 2.4 Integration; 2.5 The Lp Spaces; 2.6 Applications; Problems; Chapter 3. Foundations of Linear Operator Theory; 3.1 Introduction; 3.2 The Basic Terminology of Operator Theory; 3.3 Some Algebraic Properties of Linear Operators; 3.4 Continuity and Boundedness
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3.5 Some Fundamental Properties of Bounded Operators3.6 First Results on the Solution of the Equation Lf = g; 3.7 Introduction to Spectral Theory; 3.8 Closed Operators and Differential Equations; Problems; Chapter 4. Introduction to Nonlinear Operators; 4.1 Introduction; 4.2 Preliminaries; 4.3 The Contraction Mapping Principle; 4.4 The Fréchet Derivative; 4.5 Newton's Method for Nonlinear Operators; Problems; Chapter 5. Compact Sets in Banach Spaces; 5.1 Introduction; 5.2 Definitions; 5.3 Some Consequences of Compactness; 5.4 Some Important Compact Sets of Functions; Problems
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8.1 Introduction8.2 The Schauder Fixed Point Theorem; 8.3 Positive and Monotone Operators in Partially Ordered Banach Spaces; Problems; Chapter 9. The Spectral Theorem; 9.1 Introduction; 9.2 Preliminaries; 9.3 Background to the Spectral Theorem; 9.4 The Spectral Theorem for Bounded Self-adjoint Operators; 9.5 The Spectrum and the Resolvent; 9.6 Unbounded Self-adjoint Operators; 9.7 The Solution of an Evolution Equation; Problems; Chapter 10. Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations; 10.1 Introduction; 10.2 Extensions of Symmetric Operators
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10.3 Formal Ordinary Differential Operators: Preliminaries10.4 Symmetric Operators Associated with Formal Ordinary Differential Operators; 10.5 The Construction of Self-adjoint Extensions; 10.6 Generalized Eigenfunction Expansions; Problems; Chapter 11. Linear Elliptic Partial Differential Equations; 11.1 Introduction; 11.2 Notation; 11.3 Weak Derivatives and Sobolev Spaces; 11.4 The Generalized Dirichlet Problem; 11.5 Fredholm Alternative for the Generalized Dirichlet Problem; 11.6 Smoothness of Weak Solutions; 11.7 Further Developments; Problems; Chapter 12. The Finite Element Method
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12.1 Introduction
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English
Additional Edition:
ISBN 0-444-51790-1
Language:
English
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