Basic Elements of Real Analysis

1. Front Matter

   Pages i-xi

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2. The Real Number System

   Pages 1-22

3. Continuity and Limits

   Pages 23-44

4. Basic Properties of Functions on ℝ1

   Pages 45-66

5. Elementary Theory of Differentiation

   Pages 67-80

6. Elementary Theory of Integration

   Pages 81-100

7. Elementary Theory of Metric Spaces

   Pages 101-124

8. Differentiation and Integration in ℝN

   Pages 125-149

9. Infinite Series

   Pages 150-177

10. The Derivative of an Integral

    Pages 178-189

11. The Riemann-Stieltjes Integral

    Pages 190-204

12. The Implicit Function Theorem. Lagrange Multipliers

    Pages 205-213

13. Vector Functions on ℝN; The Theorems of Green and stokes

    Pages 214-259

14. Back Matter

    Pages 261-274

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From the author of the highly acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one- semester course in real analysis. Many students of mathematics and those students who intend to study any of the physical sciences and computer science need a text that presents the most important material in a brief and elementary fashion. The author has included such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed. There are illustrative examples throughout with over 45 figures.

• Implicit function
• calculus
• derivative
• differential equation
• real analysis

"This book is intended for a "shortened" course aimed at students who intend to study the physical sciences or computer science. It covers the most important topics in an elementary way. ... The book can be recommended to students desiring a good solid background in mathematics for the study of other sciences without unnecessary detours."
EMS Newsletter, June 2001

• Department of Mathematics, University of California, Berkeley, USA

  Murray H. Protter

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