# Foundations of Mathematical Analysis

## Benefits

• Questions and Exercises" are provided at the end of each section, covering a broad spectrum of content and various levels of difficulty, and hints are provided for selected exercises

• Some of the exercises are routine in nature while others are interesting, instructive, and challenging

• Covers a broad spectrum of content with a range of difficulty that would enable students to learn techniques and standard analysis tools

• Introduces convergence, continuity, differentiability, the Riemann integral, power series, uniform convergence of sequences and series of functions, and so on Examines various important applications throughout the book and uses MATHEMATICA and MAPLE to demonstrate various uses of the Fourier series

Textbook

1. Front Matter
Pages i-xv
2. S. Ponnusamy
Pages 1-21
3. S. Ponnusamy
Pages 23-70
4. S. Ponnusamy
Pages 71-113
5. S. Ponnusamy
Pages 115-146
6. S. Ponnusamy
Pages 147-207
7. S. Ponnusamy
Pages 209-270
8. S. Ponnusamy
Pages 271-329
9. S. Ponnusamy
Pages 331-369
10. S. Ponnusamy
Pages 371-427
11. S. Ponnusamy
Pages 429-467
12. S. Ponnusamy
Pages 469-505
13. Back Matter
Pages 507-570

### Introduction

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels.

This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts.

Key features include:

* “Questions and Exercises” are provided at the end of each section, covering a broad spectrum of content with various levels of difficulty;

* Some of the exercises are routine in nature while others are interesting, instructive, and challenging with hints provided for selected exercises;

* Covers a broad spectrum of content with a range of difficulty that will enable students to learn techniques and standard analysis tools;

* Introduces convergence, continuity, differentiability, the Riemann integral, power series, uniform convergence of sequences and series of functions, among other topics;

* Examines various important applications throughout the book;

* Figures throughout the book to demonstrate ideas and concepts are drawn using Mathematica.

Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.

#### Authors and affiliations

1. 1.Department of MathematicsIndian Institue of Technology MadrasChennaiIndia

### Bibliographic information

• Book Title Foundations of Mathematical Analysis
• Authors Saminathan Ponnusamy
• DOI https://doi.org/10.1007/978-0-8176-8292-7