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Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts)

Mathematical Analysis

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Description

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.

Product Specifications

Format: paperback
ASIN: 1470456680
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis
Domain: Amazon UK
Release Date: 30 October 2020
Listed Since: 07 August 2020

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Introduction to Analysis in One Variable (Pure and Applied Undergraduate Texts)

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