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Exploratory Examples for Real Analysis
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Short description/annotationSupplementary exercises and projects for use in maths labs or classes.Main descriptionContains supplementary exercises and projects designed to facilitate students' understanding of the fundamental concepts in real analysis, a subject notoriously hard for beginners. The exercises can be used in a number of ways: to motivate a lecture; to serve as a basis for in-class activities; in lab sessions where students work in small groups and submit reports of their investigations. For the last of these, programs in Maple are supplied with further ancillary material availabl...
Short description/annotation
Supplementary exercises and projects for use in maths labs or classes.
Main description
Contains supplementary exercises and projects designed to facilitate students' understanding of the fundamental concepts in real analysis, a subject notoriously hard for beginners. The exercises can be used in a number of ways: to motivate a lecture; to serve as a basis for in-class activities; in lab sessions where students work in small groups and submit reports of their investigations. For the last of these, programs in Maple are supplied with further ancillary material available via from http://www.saintmarys.edu/~jsnow/maplets.html.
Table of contents:
1. Boundedness of sets; 2. Introducing the 'epsilon definition' of least upper bound; 3. Introduction to the formal definition of convergence; 4. Experience with the definiton of the limit of a sequence; 5. Experience with the negation of the definition of convergence; 6. Algebraic combinations of sequences; 7. Conditions related to convergence; 8. Understanding the limit superior and the limit inferior; 9. Continuity and sequences; 10. Another definition of continuity; 11. Experience with the e - d definitions of continuity and limit; 12. Uniform and convergence of a sequence of functions; Appendix. Visual guides; About the authors.
Supplementary exercises and projects for use in maths labs or classes.
Main description
Contains supplementary exercises and projects designed to facilitate students' understanding of the fundamental concepts in real analysis, a subject notoriously hard for beginners. The exercises can be used in a number of ways: to motivate a lecture; to serve as a basis for in-class activities; in lab sessions where students work in small groups and submit reports of their investigations. For the last of these, programs in Maple are supplied with further ancillary material available via from http://www.saintmarys.edu/~jsnow/maplets.html.
Table of contents:
1. Boundedness of sets; 2. Introducing the 'epsilon definition' of least upper bound; 3. Introduction to the formal definition of convergence; 4. Experience with the definiton of the limit of a sequence; 5. Experience with the negation of the definition of convergence; 6. Algebraic combinations of sequences; 7. Conditions related to convergence; 8. Understanding the limit superior and the limit inferior; 9. Continuity and sequences; 10. Another definition of continuity; 11. Experience with the e - d definitions of continuity and limit; 12. Uniform and convergence of a sequence of functions; Appendix. Visual guides; About the authors.
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