Introduction to Analysis in One Variable

Introduction to Analysis in One Variable
Author :
Publisher : American Mathematical Soc.
Total Pages : 247
Release :
ISBN-10 : 9781470456689
ISBN-13 : 1470456680
Rating : 4/5 (680 Downloads)

Book Synopsis Introduction to Analysis in One Variable by : Michael E. Taylor

Download or read book Introduction to Analysis in One Variable written by Michael E. Taylor and published by American Mathematical Soc.. This book was released on 2020-08-11 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 t 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.


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