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Full-Text Articles in Physical Sciences and Mathematics
An Algebraic Approach To Derivatives, Julia Lee Roman
An Algebraic Approach To Derivatives, Julia Lee Roman
Theses & Dissertations
The purpose of this thesis is to relate a unique method of dealing with the concept of the derivative of a function. The traditional approach to teaching calculus introduces the idea of the limit of a function early in the course as evidenced in the Essential Elements of the State Board of Education of Texas which places the limit concept as the second essential element of calculus in Texas high schools (Texas Education Agency (TEA) Essential Elements 1991). The "concepts and skills associated with the derivative" (TEA Essential Elements 1991) follow immediately after the introduction of the limit of a …
Nonstandard Analysis Based Calculus, Kathleen Renae Gibson
Nonstandard Analysis Based Calculus, Kathleen Renae Gibson
Theses Digitization Project
In the first part of the project the elementary development of an extended number system called Hyperreals is discussed. The second half of this project develops the basics of Nonstandard Analysis, including the theory of ultrafilters, and the formal construction of the Hyperreals.