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Lectures on Real Analysis


Part of Australian Mathematical Society Lecture Series

  • Date Published: June 2012
  • availability: Available
  • format: Paperback
  • isbn: 9781107608528

$ 52.99

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About the Authors
  • 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.

    • Concise so that students can focus on essentials
    • Over 200 exercises varying in difficulty
    • Eases the transition to third-year courses on metric spaces and topology
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    Product details

    • Date Published: June 2012
    • format: Paperback
    • isbn: 9781107608528
    • length: 128 pages
    • dimensions: 227 x 152 x 7 mm
    • weight: 0.19kg
    • contains: 200 exercises
    • availability: Available
  • Table of Contents

    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

  • Instructors have used or reviewed this title for the following courses

    • Vector Calculus I, Vector Calculus ll
  • Author

    Finnur Lárusson, University of Adelaide
    Finnur Lárusson 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.

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