Elementary Analysis

1. Front Matter

   Pages i-viii

   PDF

2. Introduction

   • Kenneth A. Ross

   Pages 1-23

3. Sequences

   • Kenneth A. Ross

   Pages 24-86

4. Continuity

   • Kenneth A. Ross

   Pages 87-128

5. Sequences and Series of Functions

   • Kenneth A. Ross

   Pages 129-154

6. Differentiation

   • Kenneth A. Ross

   Pages 155-183

7. Integration

   • Kenneth A. Ross

   Pages 184-232

8. Back Matter

   Pages 233-264

   PDF

Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

• Differentialrechnung
• Elementary Analysis
• Integralrechnung
• calculus
• differential equation

From the reviews:

K.A. Ross

Elementary Analysis

The Theory of Calculus

"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."—MATHEMATICAL REVIEWS

"This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." (Allen Stenger, The Mathematical Association of America, June, 2008)

• Department of Mathematics, University of Oregon, Eugene, USA

  Kenneth A. Ross

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