Date of Award

Fall 1999

Document Type

Dissertation - Restricted

Degree Name

Doctor of Philosophy (PhD)


Mathematical and Statistical Sciences


In 1961, W.W. Sawyer opened his classic book What is Calculus About? with the statement: "Calculus begins with an apparently simple and harmless question, What is speed, and how can we calculate it?'" (p.3). More generally, calculus provides the tools needed to reason quantitatively about continuously changing phenomena. The derivative, the instantaneous rate of change of a function, measures the change in one quantity relative to a change in another, extending and refining the elementary mathematical idea of average rate...



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