9780201437270

Real Analysis A First Course

by
  • ISBN13:

    9780201437270

  • ISBN10:

    0201437279

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 6/1/2001
  • Publisher: Pearson

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping On Orders Over $59!
    Your order must be $59 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
  • We Buy This Book Back!
    In-Store Credit: $15.75
    Check/Direct Deposit: $15.00
List Price: $117.80 Save up to $47.12
  • Rent Book $70.68
    Add to Cart Free Shipping

    TERM
    PRICE
    DUE

Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Summary

Real Analysis, 2/eis a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the sections have been reorganized somewhat so that related ideas are grouped together better. A few additional topics have been added; most notably, functions of bounded variation, convex function, numerical methods of integration, and metric spaces. The biggest change is the number of exercises; there are now more than 1600 exercises in the text.

Table of Contents

Real Numbers
1(48)
What Is a Real Number?
2(7)
Absolute Value, Intervals, and Inequalities
9(11)
The Completeness Axiom
20(9)
Countable and Uncountable Sets
29(8)
Real-Valued Functions
37(12)
Sequences
49(32)
Convergent Sequences
49(12)
Monotone Sequences and Cauchy Sequences
61(8)
Subsequences
69(7)
Supplementary Exercises
76(5)
Limits and Continuity
81(48)
The Limit of a Function
82(11)
Continuous Functions
93(6)
Intermediate and Extreme Values
99(11)
Uniform Continuity
110(5)
Monotone Functions
115(9)
Supplementary Exercises
124(5)
Differentiation
129(34)
The Derivative of a Function
130(9)
The Mean Value Theorem
139(8)
Further Topics on Differentiation
147(9)
Supplementary Exercises
156(7)
Integration
163(46)
The Riemann Integral
165(5)
Conditions for Riemann Integrability
170(7)
The Fundamental Theorem of Calculus
177(6)
Further Properties of the Integral
183(8)
Numerical Integration
191(10)
Supplementary Exercises
201(8)
Infinite Series
209(32)
Convergence of Infinite Series
210(6)
The Comparison Tests
216(6)
Absolute Convergence
222(6)
Rearrangements and Products
228(7)
Supplementary Exercises
235(6)
Sequences and Series of Functions
241(50)
Pointwise Convergence
242(5)
Uniform Convergence
247(5)
Uniform Convergence and Inherited Properties
252(5)
Power Series
257(9)
Taylor's Formula
266(7)
Several Miscellaneous Results
273(11)
Supplemenary Exercises
284(7)
Point-Set Topology
291(50)
Open and Closed Sets
292(8)
Compact Sets
300(7)
Continuous Functions
307(9)
Miscellaneous Results
316(10)
Metric Spaces
326(15)
A Mathematical Logic 341(18)
Mathematical Theories
341(3)
Statements and Connectives
344(2)
Open Statements and Quantifiers
346(3)
Conditional Statements and Quantifiers
349(3)
Negation of Quantified Statements
352(1)
Sample Proofs
353(5)
Some Words of Advice
358(1)
B Sets and Functions 359(6)
Sets
359(2)
Functions
361(4)
C Mathematical Induction 365(12)
Three Equivalent Statements
365(2)
The Principle of Mathematical Induction
367(4)
The Principle of Strong Induction
371(3)
The Well-Ordering Property
374(2)
Some Comments on Induction Arguments
376(1)
Bibliography 377(2)
Index 379

Rewards Program

Write a Review