About the lecture

In this mini-lecture, we introduce the equation, distance = rate × time, and consider its limitations. In particular, we discuss: (i) the equation, distance = rate × time, and consider some examples; (ii) the generalised form of this rate equation, amount = rate × input, and consider some examples; (iii) the limitations these rate equations when the rate is not constant; (iv) how calculus provides a resolution to these limitations with a concept called linear approximation, which is the idea that on small scales the rate can be approximated by a constant; and (v) ‘the limit’ as a tool used when applying the concept of linear approximation.

About the lecturer

Paul T. Allen is an Associate Professor of Mathematics at Lewis & Clark College in Portland, OR. His current research interests involve studying problems in geometric analysis by analysing associated partial differential equations, many of which are related to problems in mathematical relativity.