
An Introduction to Mathematical Analysis
International Series of Monographs on Pure and Applied Mathematics
- 624 pages
- English
- PDF
- Available on iOS & Android
An Introduction to Mathematical Analysis
International Series of Monographs on Pure and Applied Mathematics
About this book
An Introduction to Mathematical Analysis is an introductory text to mathematical analysis, with emphasis on functions of a single real variable. Topics covered include limits and continuity, differentiability, integration, and convergence of infinite series, along with double series and infinite products.This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds of sets of real numbers. The following chapters deal with limits of real functions; differentiability and maxima, minima, and convexity; elementary properties of infinite series; and functions defined by power series. Integration is also considered, paying particular attention to the indefinite integral; interval functions and functions of bounded variation; the Riemann-Stieltjes integral; the Riemann integral; and area and curves. The final chapter is devoted to convergence and uniformity.This monograph is intended for mathematics students.
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Information
Table of contents
- Front Cover
- An Introduction to Mathematical Analysis
- Copyright Page
- Table of Contents
- Dedication
- PREFACE
- LIST OF SYMBOLS AND NOTATIONS
- CHAPTER 1. FUNDAMENTAL IDEAS AND ASSUMPTIONS
- CHAPTER 2. LIMITS AND CONTINUITY
- CHAPTER 3. DIFFERENTIABILITY
- CHAPTER 4. INFINITE SERIES
- CHAPTER 5. FUNCTIONS DEFINED BY POWER SERIES
- CHAPTER 6. INTEGRATION
- CHAPTER 7. CONVERGENCE AND UNIFORMITY
- HINTS FOR SOLUTIONS OF EXERCISES
- INDEX