From Calculus to Analysis

  • Rinaldo B. Schinazi

Table of contents

  1. Front Matter
    Pages I-X
  2. Rinaldo B. Schinazi
    Pages 1-32
  3. Rinaldo B. Schinazi
    Pages 33-63
  4. Rinaldo B. Schinazi
    Pages 65-94
  5. Rinaldo B. Schinazi
    Pages 95-135
  6. Rinaldo B. Schinazi
    Pages 137-176
  7. Rinaldo B. Schinazi
    Pages 177-205
  8. Rinaldo B. Schinazi
    Pages 207-219
  9. Rinaldo B. Schinazi
    Pages 221-233
  10. Rinaldo B. Schinazi
    Pages 235-244
  11. Back Matter
    Pages 245-250

About this book

Introduction

This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis.

Key features:

* Contains numerous exercises;

* Provides unique examples, such as many ways to estimate the number Pi;

* Introduces the basic principles of analysis;

* Offers a straightforward introduction to the calculus basics such as number systems, sequences, and series;

* Carefully written book with a thoughtful perspective for students.

From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.

Keywords

Bolzaano-Weirestrass theorem Euler's formula Stirling's formula Wallis' integrals absolute convergence

Authors and affiliations

  • Rinaldo B. Schinazi
    • 1
  1. 1., MathematicsUniversity of ColoradoColorado SpringsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8289-7
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Birkhäuser, Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8288-0
  • Online ISBN 978-0-8176-8289-7
  • About this book