To provide students with the necessary mathematical background to be able to model processes in the life sciences.
At the end of this unit, students should be able to:
* manipulate and make effective use of a range of standard mathematical functions;
* integrate and differentiate a range of standard mathematical functions;
* write down and analyse a range of simple mathematical models and interpret the results biologically.
Calculus (T, A); modelling (T, F, A).
Exponentials, logarithms and trigonometric functions.
First-order linear difference equations: solutions, steady states, stability; biological applications, e.g. bacterial population growth, gas exchange in the lung.
Limits and derivatives: differentiation of standard functions; product rule, quotient rule, chain rule.
Applications of derivatives, e.g. maximum sustainable yield, optimal foraging, maximising oxygen uptake.
First-order ordinary differential equations; solution by separation of variables, integrating factor; applications, e.g. rate equations, exponential growth, Bertanffy growth.