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Cover: 9781441929143 | Beginning Functional Analysis | Karen Saxe | Taschenbuch | Paperback
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Beginning Functional Analysis
Taschenbuch von Karen Saxe
Sprache: Englisch

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Beschreibung
This book is designed as a text for a first course on functional analysis for ad­ vanced undergraduates or for beginning graduate students. It can be used in the undergraduate curriculum for an honors seminar, or for a "capstone" course. It can also be used for self-study or independent study. The course prerequisites are few, but a certain degree of mathematical sophistication is required. A reader must have had the equivalent of a first real analysis course, as might be taught using [25] or [109], and a first linear algebra course. Knowledge of the Lebesgue integral is not a prerequisite. Throughout the book we use elementary facts about the complex numbers; these are gathered in Appendix A. In one spe­ cific place (Section 5.3) we require a few properties of analytic functions. These are usually taught in the first half of an undergraduate complex analysis course. Because we want this book to be accessible to students who have not taken a course on complex function theory, a complete description of the needed results is given. However, we do not prove these results.
This book is designed as a text for a first course on functional analysis for ad­ vanced undergraduates or for beginning graduate students. It can be used in the undergraduate curriculum for an honors seminar, or for a "capstone" course. It can also be used for self-study or independent study. The course prerequisites are few, but a certain degree of mathematical sophistication is required. A reader must have had the equivalent of a first real analysis course, as might be taught using [25] or [109], and a first linear algebra course. Knowledge of the Lebesgue integral is not a prerequisite. Throughout the book we use elementary facts about the complex numbers; these are gathered in Appendix A. In one spe­ cific place (Section 5.3) we require a few properties of analytic functions. These are usually taught in the first half of an undergraduate complex analysis course. Because we want this book to be accessible to students who have not taken a course on complex function theory, a complete description of the needed results is given. However, we do not prove these results.
Zusammenfassung
The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators as linear transformations on these spaces. It has been the author's goal to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed first courses in linear algebra and real analysis, and to develop the topics in their historical context.
Inhaltsverzeichnis
* Metric Spaces, Normed Spaces, Inner Product Spaces * The Topology of Metric Spaces * Measure and Integration * Fourier Analysis in Hilbert Space * An Introduction to Abstract Linear Operator Theory * Further Topics * Appendix A: Complex Numbers * Appendix B: Basic Set Theory
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 216
Reihe: Undergraduate Texts in Mathematics
Inhalt: xi
197 S.
13 s/w Illustr.
ISBN-13: 9781441929143
ISBN-10: 1441929142
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Saxe, Karen
Auflage: Softcover reprint of hardcover 1st ed. 2002
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 12 mm
Von/Mit: Karen Saxe
Erscheinungsdatum: 03.12.2010
Gewicht: 0,335 kg
preigu-id: 107253017
Zusammenfassung
The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators as linear transformations on these spaces. It has been the author's goal to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed first courses in linear algebra and real analysis, and to develop the topics in their historical context.
Inhaltsverzeichnis
* Metric Spaces, Normed Spaces, Inner Product Spaces * The Topology of Metric Spaces * Measure and Integration * Fourier Analysis in Hilbert Space * An Introduction to Abstract Linear Operator Theory * Further Topics * Appendix A: Complex Numbers * Appendix B: Basic Set Theory
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 216
Reihe: Undergraduate Texts in Mathematics
Inhalt: xi
197 S.
13 s/w Illustr.
ISBN-13: 9781441929143
ISBN-10: 1441929142
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Saxe, Karen
Auflage: Softcover reprint of hardcover 1st ed. 2002
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 12 mm
Von/Mit: Karen Saxe
Erscheinungsdatum: 03.12.2010
Gewicht: 0,335 kg
preigu-id: 107253017
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