Description
Book SynopsisIntroduction to Analysis is an ideal text for a one semester course on analysis. The book covers standard material on the real numbers, sequences, continuity, differentiation, and series, and includes an introduction to proof. The author has endeavored to write this book entirely from the student's perspective: there is enough rigor to challenge even the best students in the class, but also enough explanation and detail to meet the needs of a struggling student.
From the Author to the student:
I vividly recall sitting in an Analysis class and asking myself, What is all of this for?' or I don't have any idea what's going on.' This book is designed to help the student who finds themselves asking the same sorts of questions, but will also challenge the brightest students.
Chapter 1 is a basic introduction to logic and proofs.Informal summaries of the idea of proof provided before each result, and before a solution to
Table of Contents
1. Sets, Functions, and Proofs; 2. The Real Numbers; 3. Sequences and their Limits; 4. Series of Real Numbes; 5. Limits and Continuity; 6. Differentiation; 7. Sequences and Series of Functions; A List of Commonly Used Symbols; Bibliography; Index
