An Introduction to Analysis, 4/e (GE-Paperback)

本書序言

Changes to the Exercises

• Computational exercises havebeen rewritten so that answers are simpler and easier to obtain.
• Calculus-style exercises atthe beginning of the book have been revised to be more conceptual, emphasizingthe same ideas, but at a higher level.
• Theoretical exercises ofmedium difficulty have been added throughout the book.
• New True/False questions inthe first six chapters confront common misconceptions that students sometimesacquire at this level. 

Content Updates

• A new section 1.1, Introduction,combines introductory material that was previously scattered over severalsections. This section includes two accessible examples about why proof isnecessary and why we cannot always trust what we see.
• The number of axioms hasbeen reduced from four to three by introducing the Completeness Axiom first,and using it to prove the Well Ordering Principle and the Principle ofMathematical Induction.
• The material on countable sets and inverse images of sets hasbeen postponed to Chapter 3, making it possible to begin discussing limits ofsequences even earlier than before.
• Coverage of Taylor's Formula has been moved fromChapter 7 to Chapter 4 to offer another example of the utility of the MeanValue Theorem.
• The Heine-Borel Theorem now has its own sectionand includes several exercises designed to give students practice in making alocal condition on a compact set into a global one.
• Section 12.1, Jordan regions,has been organized to simplify the presentation and make it easier to teach.

本書特色

Features

• 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 thatstudents learn the motivation behind the mathematics and are able to constructtheir own proofs.
• Early introduction of thefundamental goals of analysis Refers and examines how alimit operation interacts with algebraic operation.
• Optional appendices and enrichmentsections enables students to understand the material and allowsinstructors to tailor their courses.
• An alternate chapter on metricspaces allows instructors to cover either chapter independentlywithout mentioning the other.
• More than 200 worked examples and600 exercises encourage students to test comprehension of concepts, whileusing techniques in other contexts.
• Separate coverage of topology andanalysis presents purely computational material first, followed bytopological material in alternate chapters.
• Rigorous presentation of integers providesshorter presentations while focusing on analysis.
• Reorganized coverage of series separatesseries of constants and series of functions into separate chapters.
• Consecutive numbering of theorems,definitions and remarks allows students and instructorsto find citations easily. 

Pearson MyLab Math is not included. Students, if Pearson MyLab Math is arecommended/mandatory component of the course, please ask your instructor forthe correct ISBN. Pearson MyLab Math should only be purchased when required by aninstructor. Instructors, contact your Pearson representative for more information.

MyLab Math is not included. Students, if MyLab Math is arecommended/mandatory component of the course, please ask your instructor forthe correct ISBN. MyLab Math should only be purchased when required by aninstructor. Instructors, contact your Pearson representative for moreinformation.