A Concise Approach to Mathematical Analysis

  • Mangatiana A. Robdera

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Mangatiana A. Robdera
    Pages 1-33
  3. Mangatiana A. Robdera
    Pages 35-64
  4. Mangatiana A. Robdera
    Pages 65-94
  5. Mangatiana A. Robdera
    Pages 95-121
  6. Mangatiana A. Robdera
    Pages 123-144
  7. Mangatiana A. Robdera
    Pages 145-175
  8. Mangatiana A. Robdera
    Pages 177-211
  9. Mangatiana A. Robdera
    Pages 213-240
  10. Mangatiana A. Robdera
    Pages 241-269
  11. Mangatiana A. Robdera
    Pages 271-311
  12. Mangatiana A. Robdera
    Pages 313-338
  13. Back Matter
    Pages 339-366

About this book

Introduction

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.

Keywords

Advanced calculus Derivative Fourier series Mathematical analysis Mean value theorem Riemann integral Taylor series Taylor's theorem calculus compactness differential equation fixed-point theorem improper integral

Authors and affiliations

  • Mangatiana A. Robdera
    • 1
  1. 1.School of Science and EngineeringAl Akhawayn UniversityIfraneMorocco

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-347-3
  • Copyright Information Springer-Verlag London Limited 2003
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-552-6
  • Online ISBN 978-0-85729-347-3
  • About this book