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A Concise Approach to Mathematical Analysis

  • Textbook
  • © 2003

Overview

Authors:
  1. Mangatiana A. Robdera

    1. School of Science and Engineering, Al Akhawayn University, Ifrane, Morocco

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  • Introduces the student to the more abstract concepts of advanced calculus
  • Each topic begins with a brief introduction followed by detailed examples
  • A selection of carefully-chosen exercises gives students the opportunity to practice writing proofs.

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Numbers and Functions

    • Mangatiana A. Robdera
    Pages 1-33

  3. Sequences

    • Mangatiana A. Robdera
    Pages 35-64

  4. Series

    • Mangatiana A. Robdera
    Pages 65-94

  5. Limits and Continuity

    • Mangatiana A. Robdera
    Pages 95-121

  6. Differentiation

    • Mangatiana A. Robdera
    Pages 123-144

  7. Elements of Integration

    • Mangatiana A. Robdera
    Pages 145-175

  8. Sequences and Series of Functions

    • Mangatiana A. Robdera
    Pages 177-211

  9. Local Structure on the Real Line

    • Mangatiana A. Robdera
    Pages 213-240

  10. Continuous Functions

    • Mangatiana A. Robdera
    Pages 241-269

  11. Introduction to the Lebesgue Integral

    • Mangatiana A. Robdera
    Pages 271-311

  12. Elements of Fourier Analysis

    • Mangatiana A. Robdera
    Pages 313-338

  13. Back Matter

    Pages 339-366
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Keywords

About this book

A Concise Approach to Mathematical Analysis introduces the undergraduate student to the more abstract concepts of advanced calculus. The main aim of the book is to smooth the transition from the problem-solving approach of standard calculus to the more rigorous approach of proof-writing and a deeper understanding of mathematical analysis. The first half of the textbook deals with the basic foundation of analysis on the real line; the second half introduces more abstract notions in mathematical analysis. Each topic begins with a brief introduction followed by detailed examples. A selection of exercises, ranging from the routine to the more challenging, then gives students the opportunity to practise writing proofs. The book is designed to be accessible to students with appropriate backgrounds from standard calculus courses but with limited or no previous experience in rigorous proofs. It is written primarily for advanced students of mathematics - in the 3rd or 4th year of their degree - who wish to specialise in pure and applied mathematics, but it will also prove useful to students of physics, engineering and computer science who also use advanced mathematical techniques.

Reviews

From the reviews:

THE BULLETIN OF MATHEMATICS BOOKS

"It is written primarily for advanced students of mathematics – in the 3rd of 4th year of their degree – who wish to specialize in pure and applied mathematics, but it will also prove useful to students of physics, engineering and computer science who also use advanced mathematical techniques."

Authors and Affiliations

  • School of Science and Engineering, Al Akhawayn University, Ifrane, Morocco

    Mangatiana A. Robdera

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