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[资源] 【转帖】Introduction to Calculus and Classical Analysis

Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)
By

* Publisher: Springer
* Number Of Pages: 332
* Publication Date: 2007-03
* Sales Rank: 967083
* ISBN / ASIN: 0387693157
* EAN: 9780387693156
* Binding: Hardcover
* Manufacturer: Springer
* Studio: Springer

Book Description:
This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. The book contains many remarkable features: - complete avoidance of /epsilon-/delta arguments by instead using sequences, - definition of the integral as the area under the graph, while area is defined for EVERY subset of the plane, - complete avoidance of complex numbers, - heavy emphasis on computational problems, - applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more, - 344 problems with solutions in the back of the book, - interesting applications, many of which are not usually found in advanced calculus books

About the first edition:

"The treatment, however, is far from standard, and many topics are included, especially in the last chapter, that are not available in other modern elementary texts…This is a rigorous book with good motivational material and explanatory remarks. It includes 347 problems, with solutions given in a 73-page appendix…some of the most attractive material requires considerable skill in manipulation." D.H. Armitage (MathSciNet).

New in the second edition:

For the new edition, the author has corrected errors and rewritten large portions of the text. In addition, the author has introduced new topics, such as a combinatorial proof that the radius of convergence of the Bernoulli series is 2p.

"ICCA is beautifully conceived and carefully executed...[this book] has much to teach, both about mathematics and how to write mathematics." Marvin Knopp, American Mathematical Monthly.

Table of contents
The Set of Real Numbers.- Continuity.- Differentiation.- Integration.- Applications.- Solutions.- References.- Index.
http://rapidshare.com/files/26901540/springer_-_introduction_to_calculus_and_classical_analysis.rar

[ Last edited by laizuliang on 2007-12-25 at 13:04 ]

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