TY  - BOOK
AU  - Taylor, Michael E.
TI  - Introduction to analysis in one variable
T2  - Pure and applied undergraduate texts,
SN  - 9789349750623
U1  - 517.1 
PY  - 2025///
CY  - India
PB  - Universities Press
KW  - Calculus
KW  - Real functions
KW  - Functions of one variable
KW  - One-variable calculus
KW  - Elementary functions
KW  - Integrals of Riemann, Stieltjes and Lebesgue type
N1  - Includes bibliographical references (pages 243-244) and index; Readership: Undergraduates interested in analysis in one variable
N2  - 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
UR  - https://www.ams.org/bookstore/pspdf/amstext-47-toc.pdf?_gl=1*11jrang*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAwNDYzMjQkbzEkZzEkdDE3NTAwNDk4OTAkajUzJGwwJGgw
UR  - https://www.goodreads.com/book/show/59991009-introduction-to-analysis-in-one-variable?ref=nav_sb_ss_1_40#CommunityReviews
ER  -