00000cam a22000003i 4500 UP-1685594773861497476 Buklod 20071205115406.0 j|||||||||||||| | ta 180202s1997 nyua rb |||1 u|eng d 9780387948416 (iLib)UPBAG-00001190893 DLC BAG rda eng QA 300 L36 1997 Lang, Serge 1927-2005 author. Undergraduate analysis Serge Lang. Second edition. New York Springer Science + Business Media, Inc. ©1997. xv, 642 pages illustrations 25 cm Undergraduate texts in mathematics This book is a revised edition of Analysis I--Title page verso. Includes index. Part 1. 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 -- Part 2. Convergence -- VI. Normed vector spaces -- VII. Limits -- VIII. Compactness -- IX. Series -- X. The integral in one variable -- Part 3. Applications of the integral -- XI. Approximation with convolutions -- XII. Fourier series -- XIII. Improper integrals -- XIV. The Fourier integral -- Part 4. 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 -- Part 5. Multiple integration -- XX. Multiple integrals -- XXI. Differential forms. "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 disk, ordinary differential equations, 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 [actual symbol not reproducible]-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"--Jacket. Mathematical analysis. FO UPBAG UPBAG-MAIN QA 300 L36 1997 Book