Real Analysis and Functional Analysis: A Beginner's Guide

Author: Shao Guo Nian
Publisher:
Publish Date: 2002-05-01
Features: This book can serve as a teaching reference or textbook for undergraduate students majoring in Mathematics and Applied Mathematics. Chapters 6 to 8 and some parts of Chapter 9 can also be used as teaching references for graduate students in engineering taking the "Applied Functional Analysis" course. This book was gradually developed through years of teaching practice by the authors. The entire book consists of two parts: Real Analysis and Functional Analysis, divided into ten chapters. , Chapter 2 introduces some basic concepts of set theory and point-set topology; Chapters 3 to 5 cover general measure theory, measurable functions, and integration theory; Chapters 6 to 8 introduce normed linear spaces, inner product spaces, and some fundamental theorems of functional analysis; Chapter 9 provides a brief introduction to Banach algebras and the spectrum of completely continuous operators; Chapter 10 is an appendix. A certain number of exercises are provided at the end of each chapter from to Chapter 8.