California State University, San Bernardino CSUSB ScholarWorks Theses Digitization Project John M. Pfau Library 1994 Nonstandard analysis based calculus Kathleen Renae Gibson Follow this and additional works at: https://scholarworks.lib.csusb.edu/etd-project Part of the Mathematics Commons Recommended Citation Gibson, Kathleen Renae, "Nonstandard analysis based calculus" (1994). Theses Digitization Project. 915. https://scholarworks.lib.csusb.edu/etd-project/915 This Project is brought to you for free and open access by the John M. Pfau Library at CSUSB ScholarWorks. It has been accepted for inclusion in Theses Digitization Project by an authorized administrator of CSUSB ScholarWorks. For more information, please contact
[email protected]. NONSTANDARD ANALYSIS BASED CALCULUS A Project Presented to the Faculty of California State University, San Bernardino In Partial Fulfillment of the Requirements for the Degree Master of Arts in Mathematics by Kathleen Renae Gibson November 2, 1994 NONSTANDARD ANALYSIS BASED CALCULUS A Project Presented to the Faculty of California State University, San Bernardino by Kathleen Renae Gibson November 2, 1994 Approved by: H- Dr. P. Vicknair, Chair, Mathematics Date Dr. T. Hallett, Masters Coordinator Date Dr. S. Addington, Advisor Date Dr. D. Rinne, Committee Member Date Dr. C. Frieling, Committee Member Date ABSTRACT This project seeks to present the basic approach to teaching the Calculus using concepts from Nonstandard Analysis, as developed in the text, "Elementary Calculus, An Infinitesimal Approach", by Jerome Keisler. In this first part of the project the elementary development of an extended number system called the Hyperreals is discussed. The Hyperreals, which contain infinitesimal and infinite numbers, are developed and it is shown how these numbers are used to replace limits in Calculus computations.