The rest of the course is in four sections. Modelling with mathematics starts from situations in the natural and designed worlds that can be modelled by mathematics. The models use such mathematics as the properties and representations of arithmetic and geometric sequences, lines and circles, and functions such as x 2, sin x , cos x and exp x . Discrete models deals with population models and their long-term behaviour, and introduces the arithmetic of matrices and vectors in order to examine the interdependence of subpopulations of different ages. Vectors are also used to model problems involving various physical quantities, such as forces.
Continuous models covers calculus and introduces the process of differentiation.
Standard derivatives are obtained for the functions you met in Modelling with mathematics , and are used to model motion and in optimization problems. A bank of standard integrals is obtained, and these are applied to solve simple differential equations, to find areas and in other modelling contexts. Modelling uncertainty is about probability and statistics. A chapter on chance invokes intuitive ideas of randomness and adds to your experience of thinking about probability through the use of purpose-designed software. This is followed by computer-aided exploration of sampling and sampling distributions and by an examination of regression.