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Elements of Real Analysis

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Synopses & Reviews

Publisher Comments:

Elementary Real Analysis Is A Core Course In Nearly All Mathematics Departments Throughout The World. It Enables Students To Develop A Deep Understanding Of The Key Concepts Of Calculus From A Mature Perspective. Elements Of Real Analysis Is A Student-Friendly Guide To Learning All The Important Ideas Of Elementary Real Analysis, Based On The Author's Many Years Of Experience Teaching The Subject To Typical Undergraduate Mathematics Majors. It Avoids The Compact Style Of Professional Mathematics Writing, In Favor Of A Style That Feels More Comfortable To Students Encountering The Subject For The First Time. It Presents Topics In Ways That Are Most Easily Understood, Without Sacrificing Rigor Or Coverage. In Using This Book, Students Discover That Real Analysis Is Completely Deducible From The Axioms Of The Real Number System. They Learn The Powerful Techniques Of Limits Of Sequences As The Primary Entry To The Concepts Of Analysis, And See The Ubiquitous Role Sequences Play In Virtually All Later Topics. They Become Comfortable With Topological Ideas, And See How These Concepts Help Unify The Subject. Students Encounter Many Interesting Examples, Including Pathological Ones, That Motivate The Subject And Help Fix The Concepts. They Develop A Unified Understanding Of Limits, Continuity, Differentiability, Riemann Integrability, And Infinite Series Of Numbers And Functions.

Book News Annotation:

Elementary real analysis deserves its place as a core subject in the undergraduate mathematics curriculum because of the way it provides a rigorous foundation for the theory of calculus through logical deduction from the properties of the real number system, yet most textbooks on the subject treat it with the writing style of professional mathematics, unsuited to students at the undergraduate level, according to Denlinger (Millersville U.), who here addresses that situation by presenting a text with conversational exposition, emphasis on the underlying ideas and unity of the subject, proofs written in a style appropriate for undergraduate homework, and adoption of logical symbolism intended to aid the student in recognizing formal patterns of thinking, among other pedagogical features. Prerequisites include the usual core courses in calculus and linear algebra and at least one "transitional" course utilizing logic and proof techniques. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN:
9780763779474
Author:
Denlinger, Charles G.
Publisher:
Jones & Bartlett Publishers
Author:
Denlinger, Charles
Subject:
Advanced
Subject:
Functions of real variables
Subject:
Mathematical Analysis
Subject:
Calculus
Subject:
Mathematics-Calculus
Copyright:
Publication Date:
20100531
Binding:
TRADE PAPER
Language:
English
Pages:
739

Related Subjects


Reference » Science Reference » General
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Elements of Real Analysis New Hardcover
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