Elementary Calculus: An Infinitesimal Approach - References

References

• Bishop, Errett (1977), "Review: H. Jerome Keisler, Elementary calculus", Bull. Amer. Math. Soc. 83: 205–208
• Blass, Andreas (1978), "Review: Martin Davis, Applied nonstandard analysis, and K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, and H. Jerome Keisler, Foundations of infinitesimal calculus", Bull. Amer. Math. Soc. 84 (1): 34–41

Blass writes: "I suspect that many mathematicians harbor, somewhere in the back of their minds, the formula for arc length (and quickly factor out dx before writing it down)."

• Davis, Martin (1977), "Review: J. Donald Monk, Mathematical logic", Bull. Amer. Math. Soc. 83: 1007–1011
• Davis, M.; Hausner, M (1978), "Book review. The Joy of Infinitesimals. J. Keisler's Elementary Calculus", Mathematical Intelligencer 1: 168–170 .
• Hrbacek, K.; Lessmann, O.; O’Donovan, R. (November 2010), "Analysis with Ultrasmall Numbers", American Mathematical Monthly 117 (9): 801–816
• Hrbacek, K. (2007), "Stratified Analysis?", in Van Den Berg, I.; Neves, V., The Strength of Nonstandard Analysis, Springer
• Katz, Karin Usadi; Katz, Mikhail G. (2010), "When is .999... less than 1?", The Montana Mathematics Enthusiast 7 (1): 3–30, arXiv:1007.3018
• Keisler, H. Jerome (1976), Elementary Calculus: An Approach Using Infinitesimals, Prindle Weber & Schmidt, ISBN 978-0871509116
• Keisler, H. Jerome (1976), Foundations of Infinitesimal Calculus, Prindle Weber & Schmidt, ISBN 978-0871502155, retrieved 10 jan 2007 A companion to the textbook Elementary Calculus: An Approach Using Infinitesimals.
• Keisler, H. Jerome (2011), Elementary Calculus: An Infinitesimal Approach (2nd ed.), New York: Dover Publications, ISBN 978-0-486-48452-5
• Madison, E. W.; Stroyan, K. D. (Jun.-Jul. 1977), "Elementary Calculus. by H. Jerome Keisler", The American Mathematical Monthly 84 (6): 496–500, JSTOR 2321930
• O'Donovan, R. (2007), "Pre-University Analysis", in Van Den Berg, I.; Neves, V., The Strength of Nonstandard Analysis, Springer
• O'Donovan, R.; Kimber, J. (2006), "Nonstandard analysis at pre-university level: Naive magnitude analysis", in Cultand, N; Di Nasso, M.; Ross, Nonstandard Methods and Applications in Mathematics, Lecture Notes in Logic 25 Unknown parameter |edit-first3= ignored (help)
• Stolzenberg, G. (June 1978), Notices of the American Mathematical Society 25 (4): 242
• Sullivan, Kathleen (1976), "The Teaching of Elementary Calculus Using the Nonstandard Analysis Approach", The American Mathematical Monthly (Mathematical Association of America) 83 (5): 370–375, doi:10.2307/2318657, JSTOR 2318657
• Tall, David (1980), Intuitive infinitesimals in the calculus (poster), Fourth International Congress on Mathematics Education, Berkeley