Introductory Real Analysis

Name: Introductory Real Analysis
Price: 6.26 USD
Availability: InStock
ISBN: 9780395959336

ISBN-10: 0395959330

ISBN-13: 9780395959336

Edition: 2000

Authors: Frank Dangello, Michael Seyfried

List price: $361.95

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Description:

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. Instructors will appreciate the flexibility to adjust the material to their individual class requirements. Students will benefit from reinforcing pedagogy often omitted from texts at this level.

Book details

List price: $361.95
Copyright year: 2000
Publisher: CENGAGE Learning
Publication date: 7/19/1999
Binding: Hardcover
Pages: 304
Size: 7.50" wide x 9.25" long x 0.50" tall
Weight: 1.650
Language: English




Proofs, Sets, and Functions Proofs Sets Functions Mathematical Induction



The Structure of R Algebraic and Other Properties of R


The Completeness Axiom


The Rational Numbers Are Dense in R Cardinality



Sequences


Convergence Limit Theorems Subsequences


Monotone Sequences


Bolzano-Weierstrass Theorems Cauchy Sequences


Limits at Infinity Limit Superior and Limit Inferior



Continuity


Continuous Functions


Continuity and Sequences


Limits of Functions


Consequences of Continuity


Uniform Continuity


Discontinuities and Monotone Functions



Differentiation


The Derivative Mean Value Theorems


Taylor's Theorem


L'Hopital's Rule



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



Infinite Series


Convergence and Divergence


Absolute and Conditional Convergence


Regrouping and Rearranging Series


Multiplication of Series



Sequences and Series of Functions


Function Sequences Preservation Theorems Series of Functions


Weierstrass Approximation Theorem



Power Series


Convergence Taylor Series



The Riemann-Stieltjes Theorem


Monotone Increasing


Integrators Families of Intergrable


Functions Riemann-Stieltjes Sums


Functions of Bounded Variation


Integrators of Bounded Variations



The Topology of R Open and Closed Sets


Neighborhoods and Accumulation Points Compact Sets


Connected Sets


Continuous Functions


Bibliography


Hints and Answers


Index