Course Details in 2024/25 Session

Module Title	LH Engineering Mathematics 3
School	School of Engineering
Department	Mechanical Engineering
Module Code	04 23779
Module Lead	Sam Johnson and Galane Luo
Level	Honours Level
Credits	20
Semester	Semester 2
Pre-requisites
Co-requisites
Restrictions	None
Contact Hours	Lecture-40 hours Tutorial-10 hours Supervised time in studio/workshop-10 hours Guided independent study-140 hours Total: 200 hours
Exclusions
Description	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.
Learning Outcomes	By the end of the module students should be able to: 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.
Assessment	23779-22 : Quiz 1 : Class Test (10%) 23779-23 : Quiz 2 : Class Test (10%) 23779-24 : Exam : Exam (Centrally Timetabled) - Written Unseen (80%)
Assessment Methods & Exceptions	Assessment: Assessments: 20% Continuous assessment (comprising two class tests, 10% each). 80% by 2-hour closed book centrally timetabled exam in May/June assessment period if this is possible. Reassessment: 100% exam in the supplementary period
Other	None
Reading List