عنوان
پدید آورنده
موضوع
رده
QA303.2 .E73 2018eb
QA303
.
2
.
E73
2018eb
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
1470447622
(Number (ISBN
9781470447625
Erroneous ISBN
1470442469
Erroneous ISBN
9781470442460
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
A problems based course in advanced calculus /
General Material Designation
[Book]
First Statement of Responsibility
John M. Erdman.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Providence, Rhode Island :
Name of Publisher, Distributor, etc.
American Mathematical Society,
Date of Publication, Distribution, etc.
[2018]
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (xix, 360 pages)
SERIES
Series Title
Pure and applied undergraduate texts ;
Series Title
The Sally series
Volume Designation
32
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Cover; Title page; Contents; Preface; For students: How to use this book; Chapter 1. Intervals; 1.1. Distance and neighborhoods; 1.2. Interior of a set; Chapter 2. Topology of the real line; 2.1. Open subsets of \R; 2.2. Closed subsets of \R; Chapter 3. Continuous functions from \R to \R; 3.1. Continuity-as a local property; 3.2. Continuity-as a global property; 3.3. Functions defined on subsets of \R; Chapter 4. Sequences of real numbers; 4.1. Convergence of sequences; 4.2. Algebraic combinations of sequences; 4.3. Sufficient condition for convergence; 4.4. Subsequences
Text of Note
14.1. Continuous functions14.2. Maps into and from products; 14.3. Limits; Chapter 15. Compact metric spaces; 15.1. Definition and elementary properties; 15.2. The extreme value theorem; 15.3. Dini's theorem; Chapter 16. Sequential characterization of compactness; 16.1. Sequential compactness; 16.2. Conditions equivalent to compactness; 16.3. Products of compact spaces; 16.4. The Heine-Borel theorem; Chapter 17. Connectedness; 17.1. Connected spaces; 17.2. Arcwise connected spaces; Chapter 18. Complete spaces; 18.1. Cauchy sequences; 18.2. Completeness; 18.3. Completeness vs. compactness
Text of Note
9.3. Equivalent metricsChapter 10. Interiors, closures, and boundaries; 10.1. Definitions and examples; 10.2. Interior points; 10.3. Accumulation points and closures; Chapter 11. The topology of metric spaces; 11.1. Open and closed sets; 11.2. The relative topology; Chapter 12. Sequences in metric spaces; 12.1. Convergence of sequences; 12.2. Sequential characterizations of topological properties; 12.3. Products of metric spaces; Chapter 13. Uniform convergence; 13.1. The uniform metric on the space of bounded functions; 13.2. Pointwise convergence; Chapter 14. More on continuity and limits
Text of Note
Chapter 19. A fixed point theorem19.1. The contractive mapping theorem; 19.2. Application to integral equations; Chapter 20. Vector spaces; 20.1. Definitions and examples; 20.2. Linear combinations; 20.3. Convex combinations; Chapter 21. Linearity; 21.1. Linear transformations; 21.2. The algebra of linear transformations; 21.3. Matrices; 21.4. Determinants; 21.5. Matrix representations of linear transformations; Chapter 22. Norms; 22.1. Norms on linear spaces; 22.2. Norms induce metrics; 22.3. Products; 22.4. The space \fml (,); Chapter 23. Continuity and linearity
Text of Note
Chapter 5. Connectedness and the intermediate value theorem5.1. Connected subsets of \R; 5.2. Continuous images of connected sets; 5.3. Homeomorphisms; Chapter 6. Compactness and the extreme value theorem; 6.1. Compactness; 6.2. Examples of compact subsets of \R; 6.3. The extreme value theorem; Chapter 7. Limits of real valued functions; 7.1. Definition; 7.2. Continuity and limits; Chapter 8. Differentiation of real valued functions; 8.1. The families \lobo and \lobo; 8.2. Tangency; 8.3. Linear approximation; 8.4. Differentiability; Chapter 9. Metric spaces; 9.1. Definitions; 9.2. Examples
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SUMMARY OR ABSTRACT
Text of Note
This textbook is suitable for a course in advanced calculus that promotes active learning through problem solving. It can be used as a base for a Moore method or inquiry based class, or as a guide in a traditional classroom setting where lectures are organized around the presentation of problems and solutions. This book is appropriate for any student who has taken (or is concurrently taking) an introductory course in calculus. The book includes sixteen appendices that review some indispensable prerequisites on techniques of proof writing with special attention to the notation used the course.
OTHER EDITION IN ANOTHER MEDIUM
Title
Problems based course in advanced calculus.
International Standard Book Number
9781470442460
PARALLEL TITLE PROPER
Parallel Title
Advanced calculus
TOPICAL NAME USED AS SUBJECT
Calculus-- Study and teaching (Graduate)
Calculus, Textbooks.
Calculus.
General-- General and miscellaneous specific topics-- Problem books.
General-- Instructional exposition (textbooks, tutorial papers, etc.)
MATHEMATICS-- Calculus.
MATHEMATICS-- Mathematical Analysis.
(SUBJECT CATEGORY (Provisional
MAT-- 005000
MAT-- 034000
DEWEY DECIMAL CLASSIFICATION
Number
515
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA303
.
2
Book number
.
E73
2018eb
OTHER CLASS NUMBERS
Class number
00-01
System Code
msc
PERSONAL NAME - PRIMARY RESPONSIBILITY
Erdman, John M.,1935-
ORIGINATING SOURCE
Date of Transaction
20200823025828.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
