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  3. Lectures on Real Analysis
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  • Publisher:
    Cambridge University Press
    Publication date:
    August 2012
    June 2012
    ISBN:
    9781139208604
    9781107026780
    9781107608528
    DOI:
    https://doi.org/10.1017/CBO9781139208604
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.32kg, 128 Pages
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.19kg, 128 Pages
    • Subjects:
    Mathematics (general), Mathematics, Real and Complex Analysis
    Series:
    Australian Mathematical Society Lecture Series (21)
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    Subjects:
    Mathematics (general), Mathematics, Real and Complex Analysis
    Series:
    Australian Mathematical Society Lecture Series (21)
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    Book 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.

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