Mathematical Methods and Models: Block 4.

This block contains units 13 - 16Unit 13 Modelling with Non-linear Differential EquationsThis unit explores the mathematical models associated with two physical systems: the growth of two interacting populations, predator and prey, and the motion of a rigid pendulum. This is demonstrated through Lotka-Volterra equations, which apply to a pair of interacting populations. How can these equations be linearized near an equilibrium state and the solutions represented graphically?Unit 14 Modelling Motion in Two and Three DimensionsThis unit focusses on to motion and forces in more than one dimension. It draws on ideas about vectors, forces and component forces and fundamental ideas about mechanics of particles, in particular Newton's second law. There is also mention of kinetic energy and potential energy. The video sequences associated with this unit are available on the DVD (order code MST209/DVDR01), though it is not essential for you to view these.Unit 15 Modelling Heat TransferThis unit makes use of ideas relating to energy and first-order differential equations. It begins by developing models that could be used to answer questions such as:How much does it cost to heat up a tank full of hot water?What thickness of insulation should be applied to a hot-water tank?Is it better to insulate the roof, insulate the walls or double-glaze the windows of my house?To answer these questions we must consider the transfer of heat energy between different regions of space. This unit introduces the basic ideas of heat energy and temperature, discussing conduction, convection and radiation.Unit 16 Interpretation of Mathematical ModelsThis unit introduces the ideas of mathematical modelling. It discusses the five key stages of the mathematical modelling process in detail and looks at dimensions and units of physical quantities to see how they can be used to predict and check the outcomes of the modelling process.