02443aam a2200229 4500999001900000008004500019020001800064082001400082100002800096245002700124250000800151260002900159300006200188440004700250504024800297520136800545650003401913650004201947650002201989942001202011952019002023 c214701d214701200224b 2016 ||||| |||| 00| 0 eng d a9781493927111 a515bA2U6 aAbbott, Stephen9394091 aUnderstanding analysis a2nd bSpringerc2016aNew York axii, 312 p.bIncludes bibliographical reference and index aUndergraduate texts in mathematics9394092 aTable of Content
Preface
1 The Real Numbers
2 Sequences and Series
3 Basic Topology of R
4 Functional Limits and Continuity
5 The Derivative
6 Sequences and Series of Functions
7 The Riemann Integral
8 Additional Topics
Bibliography
Index.
aThis lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigour, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.
Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.
https://www.springer.com/gp/book/9781493927111 aMathematical analysis9394093 aGlobal analysis (Mathematics)9394094 aFunctions9394095 2ddccBK 00102ddc406515_000000000000000_A2U6708NFIC9366235aVSLbVSLcGENd2020-02-24e19g2.00kSlot 1370 (0 Floor, East Wing)l2m2o515 A2U6p201527r2020-12-08s2020-11-20v3720.67yBK