Can I read Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts) on EtoBox?

Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts) by Michael Eugene Taylor is a nonfiction available to read on EtoBox.

What is Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts) about?

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 $(\mathrm{exp}\thinspace it)$, 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.

Who reads Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts)?

Author

Michael Eugene Taylor

Publisher

American Mathematical Society

Published

2020

Language

EN

ISBN

9781470460174

Category

nonfiction

Subjects

Mathematics, Stem