A Concrete Approach to Classical Analysis

  • Marian Mureşan

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Marian Mureşan
    Pages 1-40
  3. Marian Mureşan
    Pages 41-71
  4. Marian Mureşan
    Pages 73-145
  5. Marian Mureşan
    Pages 147-190
  6. Marian Mureşan
    Pages 191-249
  7. Marian Mureşan
    Pages 251-287
  8. Marian Mureşan
    Pages 289-323
  9. Marian Mureşan
    Pages 355-379
  10. Marian Mureşan
    Pages 381-409
  11. Back Matter
    Pages 411-433

About this book

Introduction

Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science.

 

The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems.

 

The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.

Keywords

calculus differential calculus integral mathematical analysis metric space

Authors and affiliations

  • Marian Mureşan
    • 1
  1. 1.Faculty of Mathematics & Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-78933-0
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-78932-3
  • Online ISBN 978-0-387-78933-0
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152
  • About this book