Introduction to Analysis in One Variable

Michael E. Taylor

ISBN 10: 1470456680 / ISBN 13: 9781470456689

Published by American Mathematical Society, US, 2020

About this Item

This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit)(expit), for real tt, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone-Weierstrass theorem, and Fourier series.

Seller Inventory # LU-9781470456689

Bibliographic Details

• Title: Introduction to Analysis in One Variable
• Publisher: American Mathematical Society, US
• Publication Date: 2020
• Language: English
• ISBN 10: 1470456680
• ISBN 13: 9781470456689
• Binding: Paperback
• Condition: New

About this title

Synopsis

This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit), for real t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone Weierstrass theorem, and Fourier series.