Lectures on Real Analysis

Lectures on Real Analysis

  • Electronic book text
By (author) 

List price: US$32.00

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 1139512749
  • 9781139512749

Table of contents

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.show more

About Finnur Larusson

Finnur Larusson has lectured in pure mathematics at all levels, from first-year calculus to postgraduate courses, at universities in Australia, Canada and the United States. He is currently Associate Professor in the School of Mathematics at the University of Adelaide.show more