Analysis II: 3rd Edition

Analysis II: 3rd Edition Front Cover
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220 pages

Book Description

This is part two of a two-volume book on real and is intended for senior undergraduate students of mathematics who have already been exposed to . The emphasis is on rigour and foundations of . Beginning with the of the number and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann ), through to power series, several variable calculus and , and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Table of Contents

Chapter 1 Metric spaces
Chapter 2 Continuous functions on metric spaces
Chapter 3 Uniform convergence
Chapter 4 Power series
Chapter 5 Fourier series
Chapter 6 Several variable differential calculus
Chapter 7 Lebesgue measure
Chapter 8 Lebesgue integration

Book Details

  • Title: Analysis II: 3rd Edition
  • Author:
  • Length: 220 pages
  • Edition: 1st ed. 2016
  • Language: English
  • Publisher:
  • Publication Date: 2016-09-21
  • ISBN-10: 9811018030
  • ISBN-13: 9789811018039
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