Introduction to analysis in one variable
Material type:
TextSeries: Pure and applied undergraduate texts ; 47 | The Sally seriesPublication details: India : Universities Press, 2025. Description: xii, 247 pages : illustrations ; 26 cmISBN: 9789349750623Subject(s): Calculus | Real functions -- Functions of one variable -- One-variable calculus | Elementary functions | Real functions -- Integrals of Riemann, Stieltjes and Lebesgue typeDDC classification: 517.1 Online resources: Table of Contents | Reviews Summary: 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 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
NBHM Books
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SMS Library | 517.1 TAY-I (Browse shelf(Opens below)) | Available | N498 |
Includes bibliographical references (pages 243-244) and index.
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 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.
Readership: Undergraduates interested in analysis in one variable.
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