Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts, Band 47)
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| Yazar | Michael E. Taylor |
|---|---|
| Yayın Evi | American Mathematical Society |
ERWIN N GRISWOLD Book on Demand Ltd. Kolektif İspanyolca İngilizce Türkçe Rusça ROBERT H BORK Additional Contributors Gale, U.S. Supreme Court Records Springer MDPI AG Independently published LAP LAMBERT Academic Publishing Almanca Fransızca WADE H MCCREE HACHETTE LIVRE-BNF
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| Yazar | Michael E. Taylor |
|---|---|
| İsbn 10 | 1470456680 |
| İsbn 13 | 978-1470456689 |
| Yayın Evi | American Mathematical Society |
| tarafından gönderildi Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts, Band 47) | 9 Ekim 2020 |
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.
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