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BL
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| Record Number
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850303
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| Main Entry
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Erdman, John M.,1935-
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| Title & Author
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A problems based course in advanced calculus /\ John M. Erdman.
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| Publication Statement
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Providence, Rhode Island :: American Mathematical Society,, [2018]
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| Series Statement
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Pure and applied undergraduate texts ;; 32
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The Sally series
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| Page. NO
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1 online resource (xix, 360 pages)
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| ISBN
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1470447622
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: 9781470447625
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1470442469
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9781470442460
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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
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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
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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
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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
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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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| Abstract
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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.
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| Subject
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Calculus, Textbooks.
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Calculus-- Study and teaching (Graduate)
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Calculus.
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General-- General and miscellaneous specific topics-- Problem books.
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General-- Instructional exposition (textbooks, tutorial papers, etc.)
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| Subject
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MATHEMATICS-- Calculus.
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MATHEMATICS-- Mathematical Analysis.
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| Dewey Classification
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515
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| LC Classification
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QA303.2.E73 2018eb
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| NLM classification
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00A0700-01msc
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| Parallel Title
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Advanced calculus
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