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Cover: 9780387948416 | Undergraduate Analysis | Serge Lang | Buch | Englisch | 2005
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Undergraduate Analysis
Buch von Serge Lang
Sprache: Englisch

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Beschreibung
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises.
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises.
Zusammenfassung
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration.
Inhaltsverzeichnis
One Review of Calculus.- 0 Sets and Mappings.- I Real Numbers.- II Limits and Continuous Functions.- III Differentiation.- IV Elementary Functions.- V The Elementary Real Integral.- Two Convergence.- VI Normed Vector Spaces.- VII Limits.- VIII Compactness.- IX Series.- X The Integral in One Variable.- Three Applications of the Integral.- XI Approximation with Convolutions.- XII Fourier Series.- XIII Improper Integrals.- XIV The Fourier Integral.- Four Calculus in Vector Spaces.- XV Functions on n-Space.- XVI The Winding Number and Global Potential Functions.- XVII Derivatives in Vector Spaces.- XVIII Inverse Mapping Theorem.- XIX Ordinary Differential Equations.- Five Multiple Integration.- XX Multiple Integrals.- XXI Differential Forms.
Details
Erscheinungsjahr: 1996
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 664
Reihe: Undergraduate Texts in Mathematics
Inhalt: xv
642 S.
23 s/w Illustr.
642 p. 23 illus.
ISBN-13: 9780387948416
ISBN-10: 0387948414
Sprache: Englisch
Herstellernummer: 10544242
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lang, Serge
Auflage: 2nd ed. 1997
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 41 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 05.12.1996
Gewicht: 1,15 kg
preigu-id: 103843177
Zusammenfassung
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration.
Inhaltsverzeichnis
One Review of Calculus.- 0 Sets and Mappings.- I Real Numbers.- II Limits and Continuous Functions.- III Differentiation.- IV Elementary Functions.- V The Elementary Real Integral.- Two Convergence.- VI Normed Vector Spaces.- VII Limits.- VIII Compactness.- IX Series.- X The Integral in One Variable.- Three Applications of the Integral.- XI Approximation with Convolutions.- XII Fourier Series.- XIII Improper Integrals.- XIV The Fourier Integral.- Four Calculus in Vector Spaces.- XV Functions on n-Space.- XVI The Winding Number and Global Potential Functions.- XVII Derivatives in Vector Spaces.- XVIII Inverse Mapping Theorem.- XIX Ordinary Differential Equations.- Five Multiple Integration.- XX Multiple Integrals.- XXI Differential Forms.
Details
Erscheinungsjahr: 1996
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 664
Reihe: Undergraduate Texts in Mathematics
Inhalt: xv
642 S.
23 s/w Illustr.
642 p. 23 illus.
ISBN-13: 9780387948416
ISBN-10: 0387948414
Sprache: Englisch
Herstellernummer: 10544242
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lang, Serge
Auflage: 2nd ed. 1997
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 41 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 05.12.1996
Gewicht: 1,15 kg
preigu-id: 103843177
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