Introduction
Many models of engineering systems involve the rate of change of a quantity. There is thus a need to incorporate derivatives into the mathematical model. These mathematical models are examples of differential equations .
Accompanying the differential equation will be one or more conditions that let us obtain a unique solution to a particular problem. Often we solve the differential equation first to obtain a general solution; then we apply the conditions to obtain the unique solution. It is important to know which conditions must be specified in order to obtain a unique solution.
Prerequisites
- be able to differentiate; ( HELM booklet 11)
- be able to integrate; ( HELM booklet 13)
Learning Outcomes
- understand the use of differential equations in modelling engineering systems
- identify the order and type of a differential equation
- recognise the nature of a general solution
- determine the nature of the appropriate additional conditions which will give a unique solution to the equation
Contents
1 Case study: Newton’s law of cooling2 The general solution of a differential equation
3 Classifying differential equations