Synopses & Reviews
Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis.
Review
"...a fresh approach to a standard subject in topology and analysis...A healthy, vigorous introduction to analysis." American Scientist
Synopsis
An introductory text on metric spaces for students who are as interested in the applications as in the theory.
Synopsis
An introduction to metric spaces for those interested in the applications as well as theory.
Table of Contents
Preface; 1. Sequences by iteration; 2. Metric spaces; 3. The three Cs; 4. The contraction mapping principle; 5. What makes analysis work?; Index.