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Applications of Functional Analysis and Operator Theory, Volume 200, Second Edition (Mathematics in Science and Engineering)
 
 

Applications of Functional Analysis and Operator Theory, Volume 200, Second Edition (Mathematics in Science and Engineering) [Hardcover]

V. Hutson (Author), J. Pym (Author), M. Cloud (Author)

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Book Description

0444517901 978-0444517906 April 22, 2005 2
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 mathematics, the physical sciences, or engineering.
- Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
- Introduces each new topic with a clear, concise explanation.
- Includes numerous examples linking fundamental principles with applications.
- Solidifies the reader's understanding with numerous end-of-chapter problems.

· Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
· Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
· Introduces each new topic with a clear, concise explanation.
· Includes numerous examples linking fundamental principles with applications.
· Solidifies the reader's understanding with numerous end-of-chapter problems.

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Book Description

Introduces each new topic with a clear, concise explanation

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Inside This Book (learn more)
First Sentence:
One of the earliest successes of an "abstract" approach to practical problems was in the discussion of the linear equation Lf = g where L is an n x n matrix and f and g are n-vectors. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
formal ordinary differential operators, generalized eigenfunction expansions, successive substitution method, deficiency indices, weak analogue, sup norm, normed vector space, continuous branch, conjugate index, spectral family, homotopy invariance, imbedding theorem, monotone increasing sequence, closed unit ball, weak derivatives, formal operator, interior regularity, linear operator theory, eigenfunction problems, closed linear span, ball centre, residual spectrum, closed extension, order interval
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Spectral Theorem, Contraction Mapping Principle, Schauder Fixed Point Theorem, Ascoli Theorem, Hahn-Banach Theorem, Hilbert-Schmidt Theorem, Implicit Function Theorem, Brouwer Fixed Point Theorem, Projection Theorem, Alternative Theorem, Mean Value Theorem, Dominated Convergence Theorem, Monotone Convergence Theorem, Open Mapping Theorem, Riesz Representation Theorem, Schauder Theorem, Problems Throughout, Sobolev Imbedding Theorem, Consider the Hammerstein
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