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A Problems Based Course in Advanced Calculus
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About This Book
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.A solutions manual is freely available electronically.
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Yes, you can access A Problems Based Course in Advanced Calculus by John M. Erdman in PDF and/or ePUB format, as well as other popular books in Mathématiques & Calcul. We have over one million books available in our catalogue for you to explore.
Information
Topic
MathématiquesSubtopic
CalculTable of contents
- Cover
- Title page
- Contents
- Preface
- For students: How to use this book
- Chapter 1. Intervals
- Chapter 2. Topology of the real line
- Chapter 3. Continuous functions from \R to \R
- Chapter 4. Sequences of real numbers
- Chapter 5. Connectedness and the intermediate value theorem
- Chapter 6. Compactness and the extreme value theorem
- Chapter 7. Limits of real valued functions
- Chapter 8. Differentiation of real valued functions
- Chapter 9. Metric spaces
- Chapter 10. Interiors, closures, and boundaries
- Chapter 11. The topology of metric spaces
- Chapter 12. Sequences in metric spaces
- Chapter 13. Uniform convergence
- Chapter 14. More on continuity and limits
- Chapter 15. Compact metric spaces
- Chapter 16. Sequential characterization of compactness
- Chapter 17. Connectedness
- Chapter 18. Complete spaces
- Chapter 19. A fixed point theorem
- Chapter 20. Vector spaces
- Chapter 21. Linearity
- Chapter 22. Norms
- Chapter 23. Continuity and linearity
- Chapter 24. The Cauchy integral
- Chapter 25. Differential calculus
- Chapter 26. Partial derivatives and iterated integrals
- Chapter 27. Computations in \Rⁿ
- Chapter 28. Infinite series
- Chapter 29. The implicit function theorem
- Chapter 30. Higher order derivatives
- Appendix A. Quantifiers
- Appendix B. Sets
- Appendix C. Special subsets of \R
- Appendix D. Logical connectives
- Appendix E. Writing mathematics
- Appendix F. Set operations
- Appendix G. Arithmetic
- Appendix H. Order properties of \R
- Appendix I. Natural numbers and mathematical induction
- Appendix J. Least upper bounds and greatest lower bounds
- Appendix K. Products, relations, and functions
- Appendix L. Properties of functions
- Appendix M. Functions that have inverses
- Appendix N. Products
- Appendix O. Finite and infinite sets
- Appendix P. Countable and uncountable sets
- Bibliography
- Index
- Back Cover