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Catalogue Information
Field name
Details
Dewey Class
515
Title
Undergraduate Analysis ([EBook]) / by Serge Lang.
Author
Lang, Serge. , 1927-2005
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer , 1983.
Physical Details
XIII, 546 pages, 17 illus. : online resource.
Series
Undergraduate texts in mathematics
0172-6056
ISBN
9781475718010
Summary Note
The present volume is a text designed for a first course in analysis. Although it is logically self-contained, it presupposes the mathematical maturity acquired by students who will ordinarily have had two years of calculus. When used in this context, most of the first part can be omitted, or reviewed extremely rapidly, or left to the students to read by themselves. The course can proceed immediately into Part Two after covering Chapters o and 1. However, the techniques of Part One are precisely those which are not emphasized in elementary calculus courses, since they are regarded as too sophisticated. The context of a third-year course is the first time that they are given proper emphasis, and thus it is important that Part One be thoroughly mastered. Emphasis has shifted from computational aspects of calculus to theoretical aspects: proofs for theorems concerning continuous 2 functions; sketching curves like x e-X, x log x, xlix which are usually regarded as too difficult for the more elementary courses; and other similar matters.:
Contents note
0 Sets and Mappings -- 1 Real Numbers -- 2 Limits and Continuous Functions -- 3 Differentiation -- 4 Elementary Functions -- 5 The Elementary Real Integral -- 6 Normed Vector Spaces -- 7 Limits -- 8 Compactness -- 9 Series -- 10 The Integral in One Variable -- 11 Approximation with Convolutions -- 12 Fourier Series -- 13 Improper Integrals -- 14 The Fourier Integral -- 15 Functions on n-Space -- 16 Derivatives in Vector Spaces -- 17 Inverse Mapping Theorem -- 18 Ordinary Differential Equations -- 19 Multiple Integrals -- 20 Differential Forms.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4757-1801-0
Links to Related Works
Subject References:
Analysis
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Analysis (Mathematics)
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Mathematical analysis
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Mathematics
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Authors:
Lang, Serge. 1927-2005
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Lang, Serge, 1927-2005.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Undergraduate texts in mathematics
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Classification:
515
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