Introduction to Analysis in One Variable - Brossura

Taylor, Michael E.

Brossura

ISBN 10: 1470456680 ISBN 13: 9781470456689

Casa editrice: Amer Mathematical Society, 2020

Riassunto

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.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2020
• Lingua: Inglese
• ISBN 10: 1470456680
• ISBN 13: 9781470456689
• Rilegatura: Copertina flessibile
• Numero di pagine: 247
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile