Research Monographs

1986 Foundations of Infinitesimal Stochastic Analysis

(with J. M. Bayod), North Holland Studies in Logic and The Foundations of Math., vol. 119, Amsterdam, 478+pgs. reviews: Bull. London Math Soc. 1989, Med. van het Wis Genootschao 1989, BAMS 1989
1976 Introduction to the Theory of Infinitesimals, (in collaboration with W. A. J. Luxemburg), Academic Press Series on Pure and Applied Math, vol 72, 321+ pgs., reviewed BAMS vol 84, nr. 1(1978), SIAM Review, vol 20, nr. 2(1978), MR vol. 58 (1979) #10429 
1998c Foundations of Infinitesimal Calculus (175 pgs.),
This short monograph is free on the web.  Follow the link above (click on the purple text).  Inside click Get Started and then look for the Mathematical Background entry on the index.  You can download as pdf.

Research Articles

1996 A Discrete Condition for Higher-Order Smoothness, with Vitor Neves, Boletim da Sociedade Portugesa de Matematica, n.35, Outtubro de 1996, p. 81-94


1995 The Infinitesimal Rule of Three, in the vol, (refereed), Developments in nonstandard analysis, Cutland, Neves, Oliveira, Sousa-Pinto editors, Pitman Research Notes in Math Sci. 336, pp. 1-22

1989 Superinfinitesimals in Topology and Functional Analysis,
(with B. Benninghofen and M. Richter), Proc. London Math Soc. (3) 59 (1989), 153-181

1987a Syntactical Methods in Infinitesimal Analysis (co-author F. Deiner), in vol., Nonstandard Analysis and its Applications, N. Cutland, ed., London Math. Soc. Student Texts vol.10, 258-281

 1987b Superinfinitesimals and Inductive Limits, ibid 1987a, 298-320

1986d Previsible Sets for Hyperfinite Filtrations, Prob. Theory and Related Fields (formerly Zeit. f. Whar.) vol. 73, 183-195

1983a Locally Convex Infinitesimal Calculus 2: Computations on Mackey(l-infinity) J. Funct. Anal., vol. 53, 1-15

1983b Myopic Utility Functions on Sequential Economies, J. of Math Econ., vol. 11, 267-276

1983c Infinitesimal Analysis of l-infinity in its Mackey Topology , in vol., Nonstandard Analysis - Recent Developments, A. Hurd, ed., Springer Verlag Lect. Notes in Math, vol. 983, New York, 204-213

1978 Infinitesimal Calculus on Locally Convex Spaces: 1. Fundamentals , Trans A M S, vol. 240, 363-383

1977 Infinitesimal Analyis of Curves and Surfaces, in vol., The Handbook of Mathematical Logic, K. J. Barwise, ed., North Holland Publ., 197-231

1974 A Nonstandard Characterization of Mixed Uniformities, in vol., Proc. of the University of Victoria Symposium on Nonstandard Analysis, A. Hurd and P. Loeb, ed.s, Springer Verlag Lect. Notes in Math, vol. 369, New York, 261-271

1973 The Mackey Uniformity m(Loo,L1) for Finite Measures, Pacific J. Math., vol 49, nr. 1, 223-228

1972a Rates of Growth of Meromorphic Functions, in vol., Contributions to Non-Standard Analysis, W. A. J. Luxemburg & A. Robinson, ed.s, North Holland Publ., Amsterdam, 47-64

1972b Additional Remarks on the Theory of Monds, ibid. 1972a, 245-260

1971 Applications of Model Theory to Complex Analysis, Ph. D. Thesis, Caltech (not published elsewhere)

Articles on Teaching

1994a Improving Success in Calculus, with J. Mathews & W. Rudolph, MAA Notes


1994b Calculus using Mathematica at Large Universities, Proceedings of the 5th ICTCM, L. Lum (editor), Addison Wesley, pp. 356-359

1992a Accelerated Calculus at the University of Iowa, CASE Newsletter, 1-3

1992b Calculus using Mathematica at the University of Iowa, Proc. of the Dennison Conf. on The Use of Symbolic Computation in Undergrad. Math, Z. Karian, ed, publ. by MAA

1991a Iowa's Computer Labs for Calculus, in vol, The Laboratory Approach to the Teaching of Calculus, L. Leinbach, ed., publ. by MAA

1991b Selecting Hardware and Software for Iowa's New Computer Labs , ibid 1991a

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