The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus.
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3 of 3 people found the following review helpful:
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A perspectiveful book,
This review is from: Applied Functional Analysis: Main Principles and Their Applications (Applied Mathematical Sciences) (Hardcover)
This excellent volume is exactly what you need to get a fast connection between traditional abstract operator theory and other application-oriented branches of mathematics. It shows how apparently different topics are in fact closely related. For example: The Hahn-Banach theorem and separation of convex sets, and eventually the optimal control of rockets; or reflexive Banach spaces and obstacle problems in elasticity; or Fredholm operators and the Navier-Stokes equations.If find this text suitable mostly for graduate students who are already acquainted with this kind of subjects and want to deepen their knowledge on the interaction between different branches of mathematics and physics. Please check my other reviews in my member page (just click on my name above).
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Inside This Book
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First Sentence:
The Hahn-Banach theorem is the most important theorem about the structure of linear continuous functionals on normed spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
outer force densities, local inverse mapping theorem, minimal stored energy, continuous inverse theorem, special product rule, closed range theorem, nonlinear monotone operators, algebraic projection, linear compact operator, sufficiently smooth solution, weight diagram, linear continuous operator, following variational problem, cubature formula, dual equation, closed linear subspace, solution iff, interpolation inequalities, gauge field theory, compact iff, modern differential geometry, multiplier rule, linear homeomorphism, multilinear forms, closed graph theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Standard Example, Hahn Banach, Analytic Operators, Compute the Euler, The Ekeland Principle New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The Hahn-Banach theorem is the most important theorem about the structure of linear continuous functionals on normed spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
outer force densities, local inverse mapping theorem, minimal stored energy, continuous inverse theorem, special product rule, closed range theorem, nonlinear monotone operators, algebraic projection, linear compact operator, sufficiently smooth solution, weight diagram, linear continuous operator, following variational problem, cubature formula, dual equation, closed linear subspace, solution iff, interpolation inequalities, gauge field theory, compact iff, modern differential geometry, multiplier rule, linear homeomorphism, multilinear forms, closed graph theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Standard Example, Hahn Banach, Analytic Operators, Compute the Euler, The Ekeland Principle New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
See all 100 books this book cites
- Periodic Motions (Applied Mathematical Sciences) by Miklos Farkas in Back Matter (1), and Back Matter (2)
- Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (Applied Mathematical Sciences) by Kenneth Meyer in Back Matter (1), and Back Matter (2)
- Differential Equations (with CD-ROM) by Paul Blanchard in Back Matter (1), and Back Matter (2)
- Infinite Dimensonal Dynamical Systems in Mechanics and Physics (Applied Mathematical Sciences) (v. 68) by Roger Temam in Back Matter (1), and Back Matter (2)
- Functional Analysis by L. V. Kantorovich in Back Matter
See all 100 books this book cites
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