Course Details in

Module Title	LH Modelling with Partial Differential Equations
School	Mathematics
Department	Mathematics
Module Code	06 27706
Module Lead	Dr David Smith
Level	Honours Level
Credits	10
Semester	Semester 2
Pre-requisites	LI Differential Equations - (06 25670) LI Multivariable & Vector Analysis - (06 25667)
Co-requisites
Restrictions	Students are prohibited from taking the level M version of this module
Contact Hours	Lecture-23 hours Tutorial-4 hours Practical Classes and workshops-2 hours Guided independent study-71 hours Total: 100 hours
Exclusions
Description	Partial differential equations describe a vast array of phenomena in nature, engineering and industry, whenever there are systems which vary in more than one dimension, e.g. space and time. Students will be introduced to a range of paradigm models from elasticity, fluid mechanics, heat transfer, chemistry, electromagnetism and traffic/crowd modelling, in many cases motivated by problems of industrial interest. A unifying theme will be the role of conservation laws in motivating models. Mathematical approaches to dimensional analysis, steady state and asymptotic simplification will be covered, in addition to analytical solutions where possible. A brief introduction to finite difference methods will be provided via a computer laboratory practical.
Learning Outcomes	By the end of the module students should be able to: Develop models of systems from verbal descriptions and conservation laws, including elasticity, fluid mechanics, heat transfer, and simple systems in chemistry and electromagnetism. Conduct dimensional analysis and exploit small/large parameter groupings. Compute analytical solutions to linear PDEs and carry out simple regular asymptotic expansions for nonlinear PDEs. Apply simple finite difference methods to compute approximate solutions to linear 2nd order differential equations.
Assessment	27706-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions	90% on a 1.5 hour examination; 10% from coursework and/or class tests. Reassessment: 100% on a 1.5 hour resit examination.
Other
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