A Concise Introduction to Analysis

✍ Scribed by Daniel W. Stroock (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 226
• Edition: 1
• Category: Library

✦ Synopsis

This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions.

✦ Table of Contents

Front Matter....Pages i-xii
Analysis on the Real Line....Pages 1-41
Elements of Complex Analysis....Pages 43-58
Integration....Pages 59-97
Higher Dimensions....Pages 99-126
Integration in Higher Dimensions....Pages 127-173
A Little Bit of Analytic Function Theory....Pages 175-208
Back Matter....Pages 209-218

✦ Subjects

Associative Rings and Algebras