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Introductory Real Analysis

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Introductory Real Analysis Cover

 

Synopses & Reviews

Publisher Comments:

This text for courses in real analysis or advanced calculus is designed specifically to present advanced calculus topics within a framework that will help students more effectively write and analyze proofs. The authors' comprehensive yet accessible presentation for one- or two-term courses offers a balanced depth of topic coverage and mathematical rigor.

Synopsis:

This text for courses in real analysis or advanced calculus is designed specifically to present advanced calculus topics within a framework that will help students more effectively write and analyze proofs. The authors' comprehensive yet accessible presentation for one- or two-term courses offers a balanced depth of topic coverage and mathematical rigor.

Table of Contents

1. Proofs, Sets, and Functions Proofs Sets Functions Mathematical Induction 2. The Structure of R Algebraic and Other Properties of R The Completeness Axiom The Rational Numbers Are Dense in R Cardinality 3. Sequences Convergence Limit Theorems Subsequences Monotone Sequences Bolzano-Weierstrass Theorems Cauchy Sequences Limits at Infinity Limit Superior and Limit Inferior 4. Continuity Continuous Functions Continuity and Sequences Limits of Functions Consequences of Continuity Uniform Continuity Discontinuities and Monotone Functions 5. Differentiation The Derivative Mean Value Theorems Taylor's Theorem L'Hôpital's Rule 6. Riemann Integration Existence of the Riemann Integral Riemann Sums Properties of the Riemann Integral Families of Riemann Integrable Functions Fundamental Theorem of Calculus Improper Integrals 7. Infinite Series Convergence and Divergence Absolute and Conditional Convergence Regrouping and Rearranging Series Multiplication of Series 8. Sequences and Series of Functions Function Sequences Preservation Theorems Series of Functions Weierstrass Approximation Theorem 9. Power Series Convergence Taylor Series 10. The Riemann-Stieltjes Theorem Monotone Increasing Integrators Families of Intergrable Functions Riemann-Stieltjes Sums Functions of Bounded Variation Integrators of Bounded Variations 11. The Topology of R Open and Closed Sets Neighborhoods and Accumulation Points Compact Sets Connected Sets Continuous Functions Bibliography. Hints and Answers. Index

Product Details

ISBN:
9780395959336
Author:
Dangello, Frank
Publisher:
Cengage Learning
Author:
Seyfried, Michael
Author:
Dangello
Author:
Dangello, Frank (Frank Dangello)
Location:
Boston :
Subject:
Mathematical Analysis
Subject:
Calculus
Subject:
Advanced
Subject:
Mathematics-Calculus
Subject:
General Mathematics
Edition Description:
Includes bibliographical references and index.
Publication Date:
19990731
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
304

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Reference » Science Reference » General
Science and Mathematics » Mathematics » Algebra » Other
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Real Analysis

Introductory Real Analysis New Hardcover
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$345.50 In Stock
Product details 304 pages Thomson Brooks/Cole - English 9780395959336 Reviews:
"Synopsis" by , This text for courses in real analysis or advanced calculus is designed specifically to present advanced calculus topics within a framework that will help students more effectively write and analyze proofs. The authors' comprehensive yet accessible presentation for one- or two-term courses offers a balanced depth of topic coverage and mathematical rigor.
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