In this module the concept of a phase space will be developed, with particular emphasis on the phase plane. We examine the theory of rigid body motions in three-spatial dimensions. We consider the time-optimal control of linear odes. Key theorems relate vector fields to their sources and give a precise characterisation of conservative vector fields. Vector calculus will be used to derive partial differential equations of mathematical physics. Methods of solving these equations will be introduced, using separation of variables. Calculus of variations will be introduced. |