An Interactive Introduction to Mathematical Analysis

This book provides a rigorous course in the calculus of functions of a real variable.

Jonathan Lewin (Author)

9781107694040, Cambridge University Press

Paperback / softback, published 23 January 2014

526 pages
17.8 x 25.4 x 2.6 cm, 1 kg

' … an exceptionally fine text.' Zentralblatt MATH

This book provides a rigorous course in the calculus of functions of a real variable. Its gentle approach, particularly in its early chapters, makes it especially suitable for students who are not headed for graduate school but, for those who are, this book also provides the opportunity to engage in a penetrating study of real analysis. The companion on-screen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The on-screen version also provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook.

1. The emergence of rigorous calculus
2. Mathematical grammar
3. Strategies for writing proofs
4. Elements of set theory
5. The real number system
6. Elementary topology of the real line
7. Limits of sequences
8. Limits and continuity of functions
9. Differentiation
10. The exponential and logarithmic functions
11. The Riemann integral
12. Infinite series
13. Improper integrals
14. Sequences and series of functions
15. Calculus of a complex variable
16. Integration of functions of two variables
17. Sets of measure zero
18. Calculus of several variables.

Subject Areas: Calculus & mathematical analysis [PBK]