• The aim of this course is to introduce students to complex functions and their applications. It will focus on properties of analytic functions, contour integration and conformal maps.
  • Many important problems in applied mathematics are modelled by systems of ordinary differential or difference equations. Even when one cannot solve these equations explicitly, it is important to know the qualitative
    properties of their solutions. Often these system depend on parameters and at critical values of the fundamental nature of the solution may change. Identifying such bifurcation points is vital to an understanding of the model.
    The topics covered in the course are:
    Equilibrium solutions, fixed points and limit cycles of a nonlinear system. Linearisation of the system about such solutions and study of their stability.
    Sketching a phase portrait for a two dimensional system.
    Bifurcations in the system as parameters change.
    Fixed points and periodic points for a nonlinear map and their stability.
    Bifurcations of nonlinear maps.