CART

(0) items

Introduction to Analysis,9780131453333
This item qualifies for
FREE SHIPPING!

FREE SHIPPING OVER $59!

Your order must be $59 or more, you must select US Postal Service Shipping as your shipping preference, and the "Group my items into as few shipments as possible" option when you place your order.

Bulk sales, PO's, Marketplace Items, eBooks, Apparel, and DVDs not included.

Introduction to Analysis

by
Edition:
4th
ISBN13:

9780131453333

ISBN10:
0131453335
Format:
Hardcover
Pub. Date:
1/1/2010
Publisher(s):
Prentice Hall
List Price: $132.00
More New and Used
from Private Sellers
Starting at $0.06

Rent Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

eTextbook

We're Sorry
Not Available

New Textbook

We're Sorry
Sold Out

Related Products


  • Introduction to Analysis
    Introduction to Analysis
  • Introduction to Analysis
    Introduction to Analysis




Summary

Offering readability, practicality and flexibility, Wade presents Fundamental Theorems from a practical viewpoint.Introduces central ideas of analysis in a one-dimensional setting, then covers multidimensional theory. Offers separate coverage of topology and analysis. Numbers theorems, definitions and remarks consecutively. Uniform writing style and notation. Practical focus on analysis.For those interested in learning more about analysis.

Table of Contents

Preface xi
Part I. ONE-DIMENSIONAL THEORY
1 The Real Number System
1(34)
1.1 Ordered field axioms
1(12)
1.2 Well-Ordering Principle
13(5)
1.3 Completeness Axiom
18(6)
1.4 Functions, countability, and the algebra of sets
24(11)
2 Sequences in R
35(23)
2.1 Limits of sequences
35(4)
2.2 Limit theorems
39(6)
2.3 Bolzano-Weierstrass Theorem
45(4)
2.4 Cauchy sequences
49(3)
2.5 Limits supremum and infimum
52(6)
3 Continuity on R
58(27)
3.1 Two-sided limits
58(8)
3.2 One-sided limits and limits at infinity
66(5)
3.3 Continuity
71(8)
3.4 Uniform continuity
79(6)
4 Differentiability on R
85(22)
4.1 The derivative
85(7)
4.2 Differentiability theorems
92(2)
4.3 Mean Value Theorem
94(8)
4.4 Monotone functions and Inverse Function Theorem
102(5)
5 Integrability on R
107(47)
5.1 Riemann integral
107(10)
5.2 Riemann sums
117(10)
5.3 Fundamental Theorem of Calculus
127(9)
5.4 Improper Riemann integration
136(6)
5.5 Functions of bounded variation
142(5)
5.6 Convex functions
147(7)
6 Infinite Series of Real Numbers
154(30)
6.1 Introduction
154(6)
6.2 Series with nonnegative terms
160(5)
6.3 Absolute convergence
165(8)
6.4 Alternating series
173(4)
6.5 Estimation of series
177(4)
6.6 Additional tests
181(3)
7 Infinite Series of Functions
184(41)
7.1 Uniform convergence of sequences
184(8)
7.2 Uniform convergence of series
192(5)
7.3 Power series
197(10)
7.4 Analytic functions
207(12)
7.5 Applications
219(6)
Part II. MULTIDIMENSIONAL THEORY
8 Euclidean Spaces
225(31)
8.1 Algebraic structure
225(9)
8.2 Planes and linear transformations
234(8)
8.3 Topology of Rn
242(7)
8.4 Interior, closure and boundary
249(7)
9 Convergence in Rn
256(34)
9.1 Limits of sequences
256(7)
9.2 Limits of functions
263(7)
9.3 Continuous functions
270(7)
9.4 Compact sets
277(3)
9.5 Applications
280(10)
10 Metric Spaces
290(31)
10.1 Introduction
290(6)
10.2 Limits of functions
296(5)
10.3 Interior, closure and boundary
301(5)
10.4 Compact sets
306(6)
10.5 Connected sets
312(4)
10.6 Continuous functions
316(5)
11 Differentiability on Rn
321(60)
11.1 Partial derivatives and partial integrals
321(11)
11.2 Definition of differentiability
332(7)
11.3 Derivatives, differentials, and tangent planes
339(9)
11.4 Chain Rule
348(4)
11.5 Mean Value Theorem and Taylor's Formula
352(6)
11.6 Inverse Function Theorem
358(11)
11.7 Optimization
369(12)
12 Integration on Rn
381(68)
12.1 Jordan regions
381(13)
12.2 Riemann integration on Jordan regions
394(13)
12.3 Iterated integrals
407(13)
12.4 Change of variables
420(12)
12.5 Partitions of unity
432(9)
12.6 Gamma function and volume
441(8)
13 Fundamental Theorems of Vector Calculus
449(57)
13.1 Curves
449(12)
13.2 Oriented curves
461(7)
13.3 Surfaces
468(11)
13.4 Oriented surfaces
479(9)
13.5 Theorems of Green and Gauss
488(8)
13.6 Stokes's Theorem
496(10)
14 Fourier Series
506(32)
14.1 Introduction
506(6)
14.2 Summability of Fourier series
512(7)
14.3 Growth of Fourier coefficients
519(7)
14.4 Convergence of Fourier series
526(6)
14.5 Uniqueness
532(6)
15 Differentiable Manifolds
538(32)
15.1 Differential forms on Rn
538(12)
15.2 Differentiable manifolds
550(11)
15.3 Stokes's Theorem on manifolds
561
Appendices
A. Algebraic laws
570(3)
B. Trigonometry
573(4)
C. Matrices and determinants
577(6)
D. Quadric surfaces
583(4)
E. Vector calculus and physics
587(3)
F. Equivalence relations
590(2)
References 592(1)
Answers and Hints to Exercises 593(18)
Subject Index 611(13)
Notation Index 624

Excerpts

This text provides a bridge from "sophomore" calculus to graduate courses that use analytic ideas, e.g., real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. For a two-semester course, the first semester should end with Chapter 8. For a three-quarter course, the second quarter should begin in Chapter 6 and end somewhere in the middle of Chapter 11. Our presentation is divided into two parts. The first half, Chapters 1 through 7 together with Appendices A and B, gradually introduces the central ideas of analysis in a one-dimensional setting. The second half, Chapters 8 through 15 together with Appendices C through F, covers multidimensional theory. More specifically, Chapter 1 introduces the real number system as a complete, ordered field, Chapters 2 through 5 cover calculus on the real line; and Chapters 6 and 7 discuss infinite series, including uniform and absolute convergence. The first two sections of Chapter 8 give a short introduction to the algebraic, structure ofR n , including the connection between linear functions and matrices. At that point instructors have two options. They can continue covering Chapters 8 and 9 to explore topology and convergence in the concrete Euclidean space setting, or they can cover these same concepts in the abstract metric space setting (Chapter 10). Since either of these options provides the necessary foundation for the rest of the book, instructors are free to choose the approach that they feel best suits their aims. With this background material out of the way, Chapters 11 through 13 develop the, machinery and theory of vector calculus. Chapter 14 gives a short introduction to Fourier series, including summability and convergence bf Fourier series, growth of Fourier coefficients, and uniqueness of trigonometric series. Chapter 15 gives a short introduction to differentiable manifolds which culminates in a proof of Stokes's Theorem on differentiable manifolds. Separating the one-dimensional from then-dimensional material is not the most efficient way to present the material, but it does have two advantages. The more abstract, geometric concepts can be postponed until students have been given a thorough introduction to analysis on the real line. Students have two chances to master some of the deeper ideas of analysis (e.g., convergence of sequences, limits of functions, and uniform continuity). We have made this text flexible in another way by including core material and enrichment material. The core material, occupying fewer than 384 pages, can be covered easily in a one-year course. The enrichment material is included for two reasons: Curious students can use it to delve deeper into the core material or as a jumping off place to pursue more general topics, and instructors can use it to supplement their course or to add variety from year to year. Enrichment material appears in enrichment sections, marked with a superscripte, or in core sections, where it is marked with an asterisk. Exercises that use enrichment material are also marked with an asterisk, and the material needed to solve them is cited in the Answers and Hints section. To make course planning easier, each enrichment section begins with a statement which indicates whether that section uses material from any other enrichment section. Since no core material depends on enrichment material, any of the latter can be skipped without loss in the integrity of the course. Most enrichment sections (5.5, 5.6, 6.5, 6.6, 7.5, 9.4, 11.6, 12.6, 14.1, 15.1) are independent and can be covered in any order after the core material that precedes them has been dealt with. Sections 9.5, 12.5, and 15.2 require 9.4, Section 15.3 requires 12.5, and Section 14.3 requires 5.5 only to establish Lemma 14.25. This result can easily be proved for continuously differentiable functions, th


Please wait while the item is added to your cart...