Real Analysis

Mark Bridger

ISBN 10: 1470451441 / ISBN 13: 9781470451448

Published by American Mathematical Society, US, 2019

About this Item

Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. For example, at the very beginning, the real numbers are shown to exist because they are constructed from the rationals using interval arithmetic. This approach, with its clear analogy to scientific measurement with tolerances, is taken throughout the book and makes the subject especially relevant and appealing to students with an interest in computing, applied mathematics, the sciences, and engineering.The first part of the book contains all the usual material in a standard one-semester course in analysis of functions of a single real variable: continuity (uniform, not pointwise), derivatives, integrals, and convergence. The second part contains enough more technical material--including an introduction to complex variables and Fourier series--to fill out a full-year course. Throughout the book the emphasis on rigorous and direct proofs is supported by an abundance of examples, exercises, and projects--many with hints--at the end of every section. The exposition is informal but exceptionally clear and well motivated throughout.

Seller Inventory # LU-9781470451448

Bibliographic Details

• Title: Real Analysis
• Publisher: American Mathematical Society, US
• Publication Date: 2019
• Language: English
• ISBN 10: 1470451441
• ISBN 13: 9781470451448
• Binding: Hardback
• Condition: New
• Weight: 752 grams

About this title

Synopsis

Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. For example, at the very beginning, the real numbers are shown to exist because they are constructed from the rationals using interval arithmetic. This approach, with its clear analogy to scientific measurement with tolerances, is taken throughout the book and makes the subject especially relevant and appealing to students with an interest in computing, applied mathematics, the sciences, and engineering. The first part of the book contains all the usual material in a standard one-semester course in analysis of functions of a single real variable: continuity (uniform, not pointwise), derivatives, integrals, and convergence. The second part contains enough more technical material including an introduction to complex variables and Fourier series to fill out a full-year course. Throughout the book the emphasis on rigorous and direct proofs is supported by an abundance of examples, exercises, and projects many with hints at the end of every section. The exposition is informal but exceptionally clear and well motivated throughout.

About the Author

Mark Bridger: Northeastern University, Boston, MA