Lectures on Real Analysis

A rigorous introduction to real analysis for undergraduates. Concise yet comprehensive, it includes a gentle introduction to metric spaces.

Finnur Lárusson (Author)

9781107608528, Cambridge University Press

Paperback / softback, published 7 June 2012

128 pages, 200 exercises
22.7 x 15.2 x 0.7 cm, 0.19 kg

This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.

Preface
To the student
1. Numbers, sets, and functions
2. The real numbers
3. Sequences
4. Open, closed, and compact sets
5. Continuity
6. Differentiation
7. Integration
8. Sequences and series of functions
9. Metric spaces
10. The contraction principle
Index.

Subject Areas: Trigonometry [PBMB], Differential calculus & equations [PBKJ], Real analysis, real variables [PBKB], Set theory [PBCH], Mathematics [PB]