Introduction to analysis in one variable
Taylor, Michael E.
Introduction to analysis in one variable - 1st Indian ed. - Rhode Island : American Mathematical Society, c2020. Hyderabad : University Press (India) Pvt. Ltd., 2025. - xii, 247 p. : ill. ; 24cm. - Pure and Applied Undergraduate Texts Vol. 47 .
Includes illustrations, appendices, bibliographic references, and subject 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 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 (exp it), 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.
9781470456689 9789349750623 (pbk.) $ 85.00 = Mathematics
Mathematics
Analysis
Functional calculus
Functions of one real variables
515.83 / TAY
Introduction to analysis in one variable - 1st Indian ed. - Rhode Island : American Mathematical Society, c2020. Hyderabad : University Press (India) Pvt. Ltd., 2025. - xii, 247 p. : ill. ; 24cm. - Pure and Applied Undergraduate Texts Vol. 47 .
Includes illustrations, appendices, bibliographic references, and subject 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 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 (exp it), 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.
9781470456689 9789349750623 (pbk.) $ 85.00 = Mathematics
Mathematics
Analysis
Functional calculus
Functions of one real variables
515.83 / TAY
