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.
Rezensionen / Stimmen
Second Edition
S. Lang
Undergraduate Analysis
"[A] fine book . . . logically self-contained . . . This material can be gone over quickly by the really well-prepared reader, for it is one of the book's pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it."-AMERICAN MATHEMATICAL SOCIETY
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Lower undergraduate
Illustrationen
23
23 s/w Abbildungen
XV, 642 p. 23 illus.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 36 mm
Gewicht
ISBN-13
978-1-4419-2853-5 (9781441928535)
DOI
10.1007/978-1-4757-2698-5
Schweitzer Klassifikation
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.
