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Module Title Applied Mathematics II Mathematics Mathematics 06 22504 Warren Smith Intermediate Level 20 Full Term none Tutorial-10 hours Lecture-46 hours Total: 56 hours 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. By the end of this module the student should be able to: use phase-plane methods to analyse second-order non-linear ordinary differential equations; formulate and analyse equations governing the motion of rigid bodies; determine the time-optimal control for a linear system of ordinary differential equations; evaluate grad, div, curl and Laplacian in both Cartesian and orthogonal curvilinear coordinates; understand and evaluate line integrals; use the integral theorems of vector analysis (Stokes', divergence and Green's theorems); recognise conservative vector fields and their properties; apply vector methods to formulate the equations of mathematical physics and solve them by using the method of separation of variables; be introduced to the calculus of variations. 22504-01 : CA Sem 1 : Coursework (10%) 22504-03 : Exam : Exam (Centrally Timetabled) - Written Unseen (80%) 22504-05 : CA Sem 2 : Class Test (10%) 80% based on a 1.5 hour unseen examination (in a joint sitting covering other optional modules.) 20% based on course work and/or class tests. none none