Real Analysis

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A Constructive Approach Through Interval Arithmetic

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Real Analysis

A Constructive Approach Through Interval Arithmetic

A unique approach to analysis that lets you apply mathematics across a range of subjects

This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. In particular, existence is never established by showing that the assumption of non-existence leads to a contradiction. The ultimate consequence of this method is that it makes sense--not just to math majors but also to students from all branches of the sciences.

The text begins with a construction of the real numbers beginning with the rationals, using interval arithmetic. This introduces readers to the reasoning and proof-writing skills necessary for doing and communicating mathematics, and it sets the foundation for the rest of the text, which includes:

Early use of the Completeness Theorem to prove a helpful Inverse Function Theorem

Sequences, limits and series, and the careful derivation of formulas and estimates for important functions

Emphasis on uniform continuity and its consequences, such as boundedness and the extension of uniformly continuous functions from dense subsets

Construction of the Riemann integral for functions uniformly continuous on an interval, and its extension to improper integrals

Differentiation, emphasizing the derivative as a function rather than a pointwise limit

Properties of sequences and series of continuous and differentiable functions

Fourier series and an introduction to more advanced ideas in functional analysis

Examples throughout the text demonstrate the application of new concepts. Readers can test their own skills with problems and projects ranging in difficulty from basic to challenging.

This book is designed mainly for an undergraduate course, and the author understands that many readers will not go on to more advanced pure mathematics. He therefore emphasizes an approach to mathematical analysis that can be applied across a range of subjects in engineering and the sciences.

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توهین به اقیلیتهای مذهبی
اهانت به مقامات سیاسی و مذهبی
اشاعه ی کودک آزاری
سایر موارد

بستن

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2019

نویسنده

Mark Bridger

ناشر

American Mathematical Society

شابک

9781470451448

20,000 تومان

خرید کتاب مطالعه نمونه درخواست ترجمه کتاب

خرید کتاب Real Analysis

Real Analysis

گزارش تخلف

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2019

نویسنده

ناشر

شابک

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