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Problems and Solutions for Undergraduate Real Analysis

Problems and Solutions for Undergraduate Real Analysis

Paperback

General Mathematics

ISBN10: 9887415537
ISBN13: 9789887415534
Publisher: Lightning Source Inc
Published: Feb 10 2020
Pages: 414
Weight: 1.57
Height: 0.85 Width: 7.00 Depth: 10.00
Language: English
The present book Problems and Solutions for Undergraduate Real Analysis is the combined volume of author's two books Problems and Solutions for Undergraduate Real Analysis I and Problems and Solutions for Undergraduate Real Analysis II. By offering 456 exercises with different levels of difficulty, this book gives a brief exposition of the foundations of first-year undergraduate real analysis. Furthermore, we believe that students and instructors may find that the book can also be served as a source for some advanced courses or as a reference.The wide variety of problems, which are of varying difficulty, include the following topics:
  • Elementary Set Algebra
  • The Real Number System
  • Countable and Uncountable Sets
  • Elementary Topology on Metric Spaces
  • Sequences in Metric Spaces
  • Series of Numbers
  • Limits and Continuity of Functions
  • Differentiation
  • The Riemann-Stieltjes Integral
  • Sequences and Series of Functions
  • Improper Integrals
  • Lebesgue Measure
  • Lebesgue Measurable Functions
  • Lebesgue Integration
  • Differential Calculus of Functions of Several Variables
  • Integral Calculus of Functions of Several Variables

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General Mathematics