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Real Variables with Basic Metric Space Topology Vital Source e-bog
Robert B. Ash
(2014)
Dover Publications
124,00 kr.
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Real Variables with Basic Metric Space Topology
Robert B. Ash
(2009)
Sprog: Engelsk
Dover Publications, Incorporated
118,00 kr.
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Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Dover Publications (Juli 2014)
- ISBN: 9780486151496
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
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Bookshelf online: 5 år fra købsdato.
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Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: -1 sider kan printes ad gangen
Copy: højest -1 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Paperback: 224 sider
- Udgiver: Dover Publications, Incorporated (Maj 2009)
- ISBN: 9780486472201
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis.
The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
INTRODUCTIONBasic TerminologyFinite and Infinite Sets; Countably Infinite and Uncountably Infinite SetsDistance and ConvergenceMinicourse in Basic LogicLimit Points and ClosureReview Problems for
Chapter 1SOME BASIC TOPOLOGICAL PROPERTIES OF RpUnions and Intersections of Open and Closed SetsCompactnessSome Applications of CompactnessLeast Upper Bounds and CompletenessReview Problems for
Chapter 2UPPER AND LOWER LIMITS OF SEQUENCES OF REAL NUMBERSGeneralization of the Limit ConceptSome Properties of Upper and Lower LimitsConvergence of Power SeriesReview Problems for
Chapter 3CONTINUOUS FUNCTIONSContinuity: Ideas, Basic Terminology, PropertiesContinuity and CompactnessTypes of DiscontinuitiesThe Cantor SetReview Problems for
Chapter 4DIFFERENTIATIONThe Derivative and Its Basic PropertiesAdditional Properties of the Derivative; Some Applications of the Mean Value TheoremReview Problems for
Chapter 5RIEMANN-STIELTJES INTEGRATIONDefinition of the IntegralProperties of the IntegralFunctions of Bounded VariationSome Useful Integration TheoremsReview Problems for
Chapter 6UNIFORM CONVERGENCE AND APPLICATIONSPointwise and Uniform ConvergenceUniform Convergence and Limit OperationsThe Weierstrass M-test and ApplicationsEquicontinuity and the Arzela-Ascoli TheoremThe Weierstrass Approximation TheoremReview Problems for
Chapter 7FURTHER TOPOLOGICAL RESULTSThe Extension ProblemBaire Category TheoremConnectednessSemicontinuous FunctionsReview Problems for
Chapter 8EPILOGUESome Compactness ResultsReplacing Cantor's Nested Set PropertyThe Real Numbers RevisitedSOLUTIONS TO PROBLEMSINDEX
Chapter 1SOME BASIC TOPOLOGICAL PROPERTIES OF RpUnions and Intersections of Open and Closed SetsCompactnessSome Applications of CompactnessLeast Upper Bounds and CompletenessReview Problems for
Chapter 2UPPER AND LOWER LIMITS OF SEQUENCES OF REAL NUMBERSGeneralization of the Limit ConceptSome Properties of Upper and Lower LimitsConvergence of Power SeriesReview Problems for
Chapter 3CONTINUOUS FUNCTIONSContinuity: Ideas, Basic Terminology, PropertiesContinuity and CompactnessTypes of DiscontinuitiesThe Cantor SetReview Problems for
Chapter 4DIFFERENTIATIONThe Derivative and Its Basic PropertiesAdditional Properties of the Derivative; Some Applications of the Mean Value TheoremReview Problems for
Chapter 5RIEMANN-STIELTJES INTEGRATIONDefinition of the IntegralProperties of the IntegralFunctions of Bounded VariationSome Useful Integration TheoremsReview Problems for
Chapter 6UNIFORM CONVERGENCE AND APPLICATIONSPointwise and Uniform ConvergenceUniform Convergence and Limit OperationsThe Weierstrass M-test and ApplicationsEquicontinuity and the Arzela-Ascoli TheoremThe Weierstrass Approximation TheoremReview Problems for
Chapter 7FURTHER TOPOLOGICAL RESULTSThe Extension ProblemBaire Category TheoremConnectednessSemicontinuous FunctionsReview Problems for
Chapter 8EPILOGUESome Compactness ResultsReplacing Cantor's Nested Set PropertyThe Real Numbers RevisitedSOLUTIONS TO PROBLEMSINDEX
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