Mathematical Modelling with Calculus

This booklet is primarily aimed at the mathematics teacher, but should also be of interest to teachers of science. It sets out a number of case studies suitable for mathematical modelling with calculus. The book starts with an explanation of the mathematical modelling process then suggests specific areas of study which include:

King Arthur's round table uses logarithms to model the process of carbon dating in order to determine the age of King Arthur’s round table.

Traffic flow uses differential equations to model braking distances of a vehicle.

Clunk-click uses formulae to explore deceleration rates during a road accident.

Optimum order quantity in which differential equations are formed and solved to determine how many components a manufacturer should order.

Single species population models in which differential equations are used to estimate population changes.

Launching a satellite in which differentiation and integration is used to model the speed required for a satellite to stay in orbit.

"Save it" - water heating and cooling in which differential equations are used to model the heating and cooling rates of water.

This resource is from the Co-operation between Science Teachers and Mathematics Teachers series produced by the ISCU Committee on the Teaching of Science.