A Problems Based Course in Advanced Calculus
eBook - PDF

A Problems Based Course in Advanced Calculus

  1. 384 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

A Problems Based Course in Advanced Calculus

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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Information

Publisher
American Mathematical Society
Year
2018
Print ISBN
9781470442460
eBook ISBN
9781470447625
Topic
Mathematics
Subtopic
Calculus
Index
Mathematics

Table of contents

  1. Cover
  2. Title page
  3. Contents
  4. Preface
  5. For students: How to use this book
  6. Chapter 1. Intervals
  7. Chapter 2. Topology of the real line
  8. Chapter 3. Continuous functions from \R to \R
  9. Chapter 4. Sequences of real numbers
  10. Chapter 5. Connectedness and the intermediate value theorem
  11. Chapter 6. Compactness and the extreme value theorem
  12. Chapter 7. Limits of real valued functions
  13. Chapter 8. Differentiation of real valued functions
  14. Chapter 9. Metric spaces
  15. Chapter 10. Interiors, closures, and boundaries
  16. Chapter 11. The topology of metric spaces
  17. Chapter 12. Sequences in metric spaces
  18. Chapter 13. Uniform convergence
  19. Chapter 14. More on continuity and limits
  20. Chapter 15. Compact metric spaces
  21. Chapter 16. Sequential characterization of compactness
  22. Chapter 17. Connectedness
  23. Chapter 18. Complete spaces
  24. Chapter 19. A fixed point theorem
  25. Chapter 20. Vector spaces
  26. Chapter 21. Linearity
  27. Chapter 22. Norms
  28. Chapter 23. Continuity and linearity
  29. Chapter 24. The Cauchy integral
  30. Chapter 25. Differential calculus
  31. Chapter 26. Partial derivatives and iterated integrals
  32. Chapter 27. Computations in \Rⁿ
  33. Chapter 28. Infinite series
  34. Chapter 29. The implicit function theorem
  35. Chapter 30. Higher order derivatives
  36. Appendix A. Quantifiers
  37. Appendix B. Sets
  38. Appendix C. Special subsets of \R
  39. Appendix D. Logical connectives
  40. Appendix E. Writing mathematics
  41. Appendix F. Set operations
  42. Appendix G. Arithmetic
  43. Appendix H. Order properties of \R
  44. Appendix I. Natural numbers and mathematical induction
  45. Appendix J. Least upper bounds and greatest lower bounds
  46. Appendix K. Products, relations, and functions
  47. Appendix L. Properties of functions
  48. Appendix M. Functions that have inverses
  49. Appendix N. Products
  50. Appendix O. Finite and infinite sets
  51. Appendix P. Countable and uncountable sets
  52. Bibliography
  53. Index
  54. Back Cover

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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 Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.