Lectures on Real Analysis

Finnur Lárusson (University of Adelaide)

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English

Cambridge University Press
07 June 2012

Mathematics & Sciences; Real analysis, real variables

Series: Australian Mathematical Society Lecture Series

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.

By: Finnur Lárusson (University of Adelaide)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 21
Dimensions: Height: 227mm, Width: 152mm, Spine: 7mm
Weight: 190g
ISBN: 9781107608528
ISBN 10: 110760852X
Series: Australian Mathematical Society Lecture Series
Pages: 128
Publication Date: 07 June 2012
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

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.

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.