This unit aims to enhance students' ability to solve the type of equations that arise from applications of mathematics to natural and technological problems by giving a grounding in perturbation techniques.
Emphasis is placed on methods of developing asymptotic solutions.
For most equations that arise in modelling applications it is unlikely that exact solutions can be found. Even convergent series approximations are often not available, or they are of limited use if they converge very slowly. They are typically divergent if summed to infinity but a few terms can often give excellent and well defined approximations. This unit introduces the basic ideas and shows how they can be applied to algebraic and differential equations, and to the evaluation of integrals. Most emphasis is placed on the latter, singular perturbations.