Lectures on Real Analysis
1st Edition
Published on 1. October 2012
128 pages
978-1-139-51274-9 (ISBN)
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
College/higher education
Illustrations
Worked examples or Exercises
File size
8735,51 MB
ISBN-13
978-1-139-51274-9 (9781139512749)
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Schweitzer Classification
Other editions
Additional editions
Finnur Larusson
Lectures on Real Analysis
Book
06/2012
Cambridge University Press
€204.60
Shipment within 15-20 days
Person
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.
Content
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.
