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040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a517.1 _bTAY-I
100			_aTaylor, Michael E.
245			_aIntroduction to analysis in one variable
260			_aIndia : _bUniversities Press, _c2025.
300			_axii, 247 pages : _billustrations ; _c26 cm.
490			_aPure and applied undergraduate texts, _v47 _x1943-9334 ;
490			_aThe Sally series
504			_aIncludes bibliographical references (pages 243-244) and index.
520			_aThis 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.
521			_aReadership: Undergraduates interested in analysis in one variable.
650			_aCalculus
650			_aReal functions _xFunctions of one variable _xOne-variable calculus
650			_aElementary functions
650			_aReal functions _xIntegrals of Riemann, Stieltjes and Lebesgue type
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/amstext-47-toc.pdf?_gl=1*11jrang*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAwNDYzMjQkbzEkZzEkdDE3NTAwNDk4OTAkajUzJGwwJGgw
856			_3Reviews _uhttps://www.goodreads.com/book/show/59991009-introduction-to-analysis-in-one-variable?ref=nav_sb_ss_1_40#CommunityReviews
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999			_c36043 _d36043