# From Calculus to Analysis

• Rinaldo B. Schinazi
Textbook

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

### 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