I'm a student
I'm an educator
Request full copy

Introduction to Analysis, An, 4th edition

Published by Pearson (March 8, 2017) © 2018

  • William R. Wade University of Tennessee

eTextbook

per month

  • Anytime, anywhere learning with the Pearson+ app
  • Easy-to-use search, navigation and notebook
  • Simpler studying with flashcards
$106.66

  • Hardcover, paperback or looseleaf edition
  • Affordable rental option for select titles
  • Free shipping on looseleafs and traditional textbooks

For 1- or 2-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis.

A modern classic

An Introduction to Analysis prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. The 4th Edition is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind the mathematics and enabling them to construct their own proofs.

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price.

Hallmark features of this title

  • Flexible presentation, with uniform writing style and notation, covers the material in small sections, allowing instructors to adapt this book to their syllabus.
  • The practical focus explains assumptions so that students learn the motivation behind the mathematics and are able to construct their own proofs.
  • Early introduction of the fundamental goals of analysis Refers and examines how a limit operation interacts with algebraic operation.
  • Optional appendices and enrichment sections enables students to understand the material and allows instructors to tailor their courses.
  • An alternate chapter on metric spaces allows instructors to cover either chapter independently without mentioning the other.
  • More than 200 worked examples and 600 exercises encourage students to test comprehension of concepts, while using techniques in other contexts.

New and updated features of this title

  • Computational exercises have been rewritten so that answers are simpler and easier to obtain.
  • Calculus-style exercises at the beginning of the book have been revised to be more conceptual, emphasizing the same ideas, but at a higher level.
  • Theoretical exercises of medium difficulty have been added throughout the book.
  • New True/False questions in the first six chapters confront common misconceptions that students sometimes acquire at this level.
  • A new section 1.1, Introduction, combines introductory material that was previously scattered over several sections. This section includes two accessible examples about why proof is necessary and why we cannot always trust what we see.
  • The number of axioms has been reduced from four to three by introducing the Completeness Axiom first, and using it to prove the Well Ordering Principle and the Principle of Mathematical Induction.

Preface

Part I. ONE-DIMENSIONAL THEORY

 

1. The Real Number System

1.1 Introduction

1.2 Ordered field axioms

1.3 Completeness Axiom

1.4 Mathematical Induction

1.5 Inverse functions and images

1.6 Countable and uncountable sets

 

2. Sequences in R

2.1 Limits of sequences

2.2 Limit theorems

2.3 Bolzano-Weierstrass Theorem

2.4 Cauchy sequences

*2.5 Limits supremum and infimum

 

3. Continuity on R

3.1 Two-sided limits

3.2 One-sided limits and limits at infinity

3.3 Continuity

3.4 Uniform continuity

 

4. Differentiability on R

4.1 The derivative

4.2 Differentiability theorems

4.3 The Mean Value Theorem

4.4 Taylor's Theorem and l'Hôpital's Rule

4.5 Inverse function theorems

 

5 Integrability on R

5.1 The Riemann integral

5.2 Riemann sums

5.3 The Fundamental Theorem of Calculus

5.4 Improper Riemann integration

*5.5 Functions of bounded variation

*5.6 Convex functions

 

6. Infinite Series of Real Numbers

6.1 Introduction

6.2 Series with nonnegative terms

6.3 Absolute convergence

6.4 Alternating series

*6.5 Estimation of series

*6.6 Additional tests

 

7. Infinite Series of Functions

7.1 Uniform convergence of sequences

7.2 Uniform convergence of series

7.3 Power series

7.4 Analytic functions

*7.5 Applications

 

Part II. MULTIDIMENSIONAL THEORY

 

8. Euclidean Spaces

8.1 Algebraic structure

8.2 Planes and linear transformations

8.3 Topology of Rn

8.4 Interior, closure, boundary

 

9. Convergence in Rn

9.1 Limits of sequences

9.2 Heine-Borel Theorem

9.3 Limits of functions

9.4 Continuous functions

*9.5 Compact sets

*9.6 Applications

 

10. Metric Spaces

10.1 Introduction

10.2 Limits of functions

10.3 Interior, closure, boundary

10.4 Compact sets

10.5 Connected sets

10.6 Continuous functions

10.7 Stone-Weierstrass Theorem

 

11. Differentiability on Rn

11.1 Partial derivatives and partial integrals

11.2 The definition of differentiability

11.3 Derivatives, differentials, and tangent planes

11.4 The Chain Rule

11.5 The Mean Value Theorem and Taylor's Formula

11.6 The Inverse Function Theorem

*11.7 Optimization

 

12. Integration on Rn

12.1 Jordan regions

12.2 Riemann integration on Jordan regions

12.3 Iterated integrals

12.4 Change of variables

*12.5 Partitions of unity

*12.6 The gamma function and volume

 

13. Fundamental Theorems of Vector Calculus

13.1 Curves

13.2 Oriented curves

13.3 Surfaces

13.4 Oriented surfaces

13.5 Theorems of Green and Gauss

13.6 Stokes's Theorem

 

*14. Fourier Series

*14.1 Introduction

*14.2 Summability of Fourier series

*14.3 Growth of Fourier coefficients

*14.4 Convergence of Fourier series

*14.5 Uniqueness

 

Appendices

A. Algebraic laws

B. Trigonometry

C. Matrices and determinants

D. Quadric surfaces

E. Vector calculus and physics

F. Equivalence relations

 

References

Answers and Hints to Exercises

Subject Index

Symbol Index

 

*Enrichment section

About our author

William Wade received his PhD in harmonic analysis from the University of California - Riverside. He has been a professor of the Department of Mathematics at the University of Tennessee for more than 40 years. During that time, he has received multiple awards including 2 Fulbright Scholarships, the Chancellor's Award for Research and Creative Achievements, the Dean's Award for Extraordinary Service, and the National Alumni Association Outstanding Teaching Award.

Wade's research interests include problems of uniqueness, growth and dyadic harmonic analysis, on which he has published numerous papers, two books and given multiple presentations on three continents. His current publication, An Introduction to Analysis, is now in its 4th edition.

In his spare time, Wade loves to travel and take photographs to document his trips. He is also musically inclined, and enjoys playing classical music, mainly baroque on the trumpet, recorder, and piano.

Need help? Get in touch

Pearson+

All in one place. Pearson+ offers instant access to eTextbooks, videos and study tools in one intuitive interface. Students choose how they learn best with enhanced search, audio and flashcards. The Pearson+ app lets them read where life takes them, no wi-fi needed. Students can access Pearson+ through a subscription or their MyLab or Mastering course.

Video
Play
Privacy and cookies
By watching, you agree Pearson can share your viewership data for marketing and analytics for one year, revocable by deleting your cookies.

Video transcript (PDF | 16KB) 

Pearson eTextbook: What’s on the inside just might surprise you

They say you can’t judge a book by its cover. It’s the same with your students. Meet each one right where they are with an engaging, interactive, personalized learning experience that goes beyond the textbook to fit any schedule, any budget, and any lifestyle. 

Digital Learning NOW

Extend your professional development and meet your students where they are with free weekly Digital Learning NOW webinars. Attend live, watch on-demand, or listen at your leisure to expand your teaching strategies. Earn digital professional development badges for attending a live session.

Explore webinars