Course Details in 2020/21 Session

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Module Title Engineering Mathematics 3 School of Engineering Mechanical Engineering 04 23779 Dr Daniel Loghin Honours Level 20 Semester 2 None Guided independent study-140 hours Supervised time in studio/workshop-10 hours Tutorial-10 hours Lecture-40 hours Total: 200 hours The aim of the module is to enhance the students’ mathematical knowledge and confidence in preparation for the demanding applications of the final stage modules, and a possible research career involving engineering science. They will develop an understanding of the numerical techniques used within modern Finite Element Analysis computer packages and develop an understanding of the mathematical basis of many of the advanced systems of equations governing engineering problems. SYLLABUS 1. Vector differential calculus: review of vectors and geometry; curvilinear coordinates; review of grad, div, curl; calculus for parametrised fields; applications: PDE of physics and engineering. 2. Vector integral calculus: line, surface, volume integrals Stokes’ theorem and Gauss’ divergence theorem; integro-differential identities; applications: length, area, volume, mass, conservation laws. 3. Numerical methods: Nonlinear iterations with application to root-finding methods: Bisection method fixed point iteration method; secant and Newton's method; interpolation by polynomials: Lagrange and Hermite interpolation; piecewise polynomial interpolation; numerical integration: Newton-Cotes rules; Gauss quadratures; product rules; numerical methods for initial value problems Euler methods; explicit Runge-Kutta methods. By the end of the module the student should be able to: Demonstrate proficiency in vector calculus, including a good understanding of 3D geometry, ability to evaluate line, surface and volume integrals as well as the ability to solve boundary value problems using some standard techniques. Demonstrate knowledge and understanding of a wide range of standard numerical techniques employed in mechanical and related engineering disciplines. 23779-05 : Exam : Exam (Centrally Timetabled) - Written Unseen (85%) 23779-20 : Semester 1 : Class Test (7.5%) 23779-21 : Semester 2 : Class Test (7.5%) Assessments: (100%) Continuous assessment (comprising two timed summative assessments, 50% each). (The final 50%: replaced by 2-hour closed book centrally timetabled exam in May/June assessment period if this is possible). None