This is a very good textbook presenting a modern course in analysis both at the advanced undergraduate and at the beginning graduate level. It contains 14 chapters, a bibliography, and an index. At the end of each chapter interesting exercises and historical notes are enclosed.\par From the cover: ``The book begins with a brief discussion of sets and mappings, describes the real number field, and proceeds to a treatment of real-valued functions of a real variable. Separate chapters are devoted to the ideas of convergent sequences and series, continuous functions, differentiation, and the Riemann integral (of a real-valued function defined on a compact interval). The middle chapters cover general topology and a miscellany of applications: the Weierstrass and Stone-Weierstrass approximation theorems, the existence of geodesics in compact metric spaces, elements of Fourier analysis, and the Weyl equidistribution theorem. Next comes a discussion of differentiation of vector-valued functions of several real variables, followed by a brief treatment of measure and integration (in a general setting, but with emphasis on Lebesgue theory in Euclidean spaces). The final part of the book deals with manifolds, differential forms, and Stokes' theorem [in the spirit of M. Spivak's: ``Calculus on manifolds'' (1965; Zbl 141.05403)] which is applied to prove Brouwer's fixed point theorem and to derive the basic properties of harmonic functions, such as the Dirichlet principle''. ZENTRALBLATT MATH
"Everything needed is clearly defined and formulated, and there is a reasonable number of examples…. Anyone teaching a year course at this level to should seriously consider this carefully written book. In the reviewer's opinion, it would be a real pleasure to use this text with such a class."—MATHEMATICAL REVIEWSFrom the Publisher:
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas.
The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.
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Descripción Springer, 1995. Estado de conservación: New. 356 pp., Hardcover, new. Nº de ref. de la librería ZB1037180
Descripción Paperback. Estado de conservación: New. New Softcover International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Nº de ref. de la librería 16841
Descripción Springer. Estado de conservación: New. Brand New! Corrected Ships fast! Expedited shipping 2-4 business days; Standard shipping 7-14 business days. Ships from USA!. Nº de ref. de la librería BER-007-140
Descripción Springer, 2001. Estado de conservación: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 1 Real Functions 2 Sequences and Series 3 Continuous Functions on Intervals 4 Differentiation 5 The Riemann Integral 6 Topology 7 Function Spaces 8 Differentiable Maps 9 Measures 10 Integration 11 Manifolds 12 Multilinear Algebra 13 Differential Forms 14 Integration on Manifolds. Nº de ref. de la librería ABE_book_new_0387946144
Descripción Springer, 2001. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería 0387946144
Descripción Springer, 1995. Hardcover. Estado de conservación: New. Corrected. This item is printed on demand. Nº de ref. de la librería DADAX0387946144
Descripción Springer 1995-12-15, 1995. Hardcover. Estado de conservación: New. Corrected. 0387946144. Nº de ref. de la librería 522223
Descripción Springer, 2001. Hardcover. Estado de conservación: New. Nº de ref. de la librería B24S4-62
Descripción Springer, 2001. Estado de conservación: New. Nº de ref. de la librería UA9780387946146
Descripción Springer Verlag, 1996. Hardcover. Estado de conservación: Brand New. 1st ed. 1996. corr. 3rd printing edition. 333 pages. 9.75x6.50x1.00 inches. In Stock. Nº de ref. de la librería __0387946144