Advanced Calculus with Linear Analysis

Joseph R. Lee

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483266589
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

Advanced Calculus with Linear Analysis provides information pertinent to the fundamental aspects of advanced calculus from the point of view of linear spaces. This book covers a variety of topics, including function spaces, infinite series, real number system, sequence spaces, power series, partial differentiation, uniform continuity, and the class of measurable sets. Organized into nine chapters, this book begins with an overview of the concept of a single-valued function, consisting of a rule, a domain, and a range. This text then describes an infinite sequence as an ordered set of elements that can be put into a one-to-one correspondence with the positive integers. Other chapters consider a normed linear space, which is complete if and only if every Cauchy sequence converges to an element in the space. This book discusses as well the convergence of an infinite series, which is determined by the convergence of the infinite sequence of partial sums. This book is a valuable resource for students.

Table of contents

• Front Cover
• Advanced Calculus with Linear Analysis
• Copyright Page
• Table of Contents
• Preface
• Acknowledgments
• Summary of Notation for Linear Spaces
• List of Elementary Symbols
• CHAPTER I. FUNCTION SPACES
• CHAPTER II. SEQUENCE SPACES AND INFINITE SERIES
• CHAPTER III. COMPLETENESS PROPERTIES
• CHAPTER IV. CONTINUOUS FUNCTIONS
• CHAPTER V. DIFFERENTIABLE FUNCTIONS
• CHAPTER VI. RIEMANN INTEGRABLE FUNCTIONS
• CHAPTER VII. INFINITE SERIES OF FUNCTIONS
• CHAPTER VIII. LEBESGUE MEASURE
• CHAPTER IX. LEBESGUE INTEGRABLE FUNCTIONS
• APPENDIX
• SUGGESTIONS FOR FUTHER READING
• SOLUTIONS TO SELECTED PROBLEMS
• Subject Index