Programme And Module Handbook
Course Details in 2021/22 Session

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Module Title LM Advanced Mathemat Modelling
Department Mathematics
Module Code 06 33873
Module Lead Dr David Smith
Level Masters Level
Credits 20
Semester Semester 1
Pre-requisites LI Differential Equations - (06 25670) LI Multivariable & Vector Analysis - (06 25667)
Restrictions None
Contact Hours Lecture-46 hours
Tutorial-10 hours
Guided independent study-144 hours
Total: 200 hours
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.

Mathematical models are used increasingly to understand complex phenomena in biology and medicine, and have been used to explain phenomena at a wide range of scales, from genes, proteins and metabolites, cells, tissues and organs, to organisms, populations and ecosystems. This module builds on the students’ knowledge of mathematical nonlinear differential and difference equations to explore the paradigm models in mathematical biology, particularly microbiology and developmental biology. The mathematical models will be linked to experimental work and biomedical science, in particular focusing on the importance of experiment in testing and refining models, in estimating parameters, and finally the application of models in making useful predictions. Topics will cover a broad spectrum of population dynamics models to be selected from predator-prey systems, enzyme kinetics, population genetics, chemical signalling, gene regulation networks, epidemiology and neuron firing.
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.
  • Students taking the module at Level M will explore the subject beyond the taught syllabus.
  • Apply core ideas (birth/replication, death/predation, catalysis, saturation, binding kinetics etc.) in the modelling of molecules, cells and organisms.
  • Formulate models of new problems using the ideas presented in the module in terms of systems of differential equations.
  • Link mathematical models to experimental work, particularly in the estimation of parameters and the testing and refining of models.
  • Analyse the dynamical properties of differential equation models systems and use these properties to make predications regarding biological and biomedical problems.
  • Students taking the module at Level M will explore the subject beyond the taught syllabus.
Assessment 33873-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions 2 hour Written Unseen January Examination (80%); In-course Assessment (20%).
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