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Viser: Undergraduate Analysis
Undergraduate Analysis
Serge A. Lang
(1996)
Sprog: Engelsk
Springer New York
685,00 kr.
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Detaljer om varen
- 2. Udgave
- Hardback: 668 sider
- Udgiver: Springer New York (December 1996)
- ISBN: 9780387948416
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. One of the author's main concerns is to achieve a balance between concrete examples and general theorems, augmented by a variety of interesting exercises. Some new material has been added in this second edition, for example: a new chapter on the global version of integration of locally integrable vector fields; a brief discussion of L1-Cauchy sequences, introducing students to the Lebesgue integral; more material on Dirac sequences and families, including a section on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises.
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.
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