Applied Functional Analysis
Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods.\ While retaining...
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Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods.While retaining the structure of its best-selling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. This edition also provides many more exercises as well as a solutions manual for qualifying instructors. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources.New to the Second Edition• Completely revised section on lim sup and lim inf• New discussions of connected sets, probability, Bayesian statistical inference, and the generalized (integral) Minkowski inequality• New sections on elements of multilinear algebra and determinants, the singular value decomposition theorem, the Cauchy principal value, and Hadamard finite part integrals• New example of a Lebesgue non-measurable setIdeal for a two-semester course, this proven textbook teaches students how to prove theorems and prepares them for further study of more advanced mathematical topics. It helps them succeed in formulating research questions in a mathematically rigorous way. Booknews Introduces the fundamental topics in functional analysis important in mathematical modeling and computer simulations, for graduate students in engineering and science with no training in advanced mathematics. Features extensive examples; exercises; narrative, intuition-building presentation; and gradual progression from elementary set theory to advanced topics including Hilbert spaces and spectral theory of linear operators. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Preface1Preliminaries1Elementary Set TheoryElementary LogicRelationsFunctionsCardinality of SetsFoundations of Abstract AlgebraElementary Topology in [actual symbol not reproducible]Elements of Differential and Integral Calculus2Linear Algebra123Vector Spaces - The Basic ConceptsLinear TransformationsAlgebraic DualsEuclidean Spaces3Lebesgue Measure and Integration215Lebesgue MeasureLebesgue Integration TheoryL[superscript p] Spaces4Topological and Metric Spaces289Elementary TopologyTheory of Metric Spaces5Banach Spaces383Topological Vector SpacesHahn-Banach Extension TheoremBounded (Continuous) Linear Operators on Normed SpacesClosed OperatorsTopological Duals. Weak CompactnessClosed Range Theorem. Solvability of Linear Equations
\ BooknewsIntroduces the fundamental topics in functional analysis important in mathematical modeling and computer simulations, for graduate students in engineering and science with no training in advanced mathematics. Features extensive examples; exercises; narrative, intuition-building presentation; and gradual progression from elementary set theory to advanced topics including Hilbert spaces and spectral theory of linear operators. Annotation c. Book News, Inc., Portland, OR (booknews.com)\ \
