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Content

Introduction to modelling Purpose of modelling; Constructing a model – problem statement, formulation, solution, validation; Illustrative examples; Decision-making with mathematical models; Arms race models; Economic models of the effect of taxation. Discrete models Discrete-time modelling; Discrete approximation of continuous-time models; Equilibria and long-run behavior; Case studies. Continuous Models Modeling with differential equations: Numerical Methods; Solving first order differential equations, generating solution curves and direction fields using mathematical software; Case studies in applications to biology and epidemiology etc. Modelling with systems of differential equations: Analysis of systems of equations using mathematical software; Case studies.

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Conditions of Participation

Knowledge of Multivariable Calculus, elementary Linear Algebra and Ordinary Differential Equations is essential for this course. As MATLAB will be utilized extensively in the compulsory computer lab sessions, an introductory course in MATLAB is also listed as a mandatory prerequisite.

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Teaching Methods

• Students will be exposed to the theoretical aspects of mathematical modelling through informative lectures. Tutorials and practical lab sessions will provide a platform for students to apply the theory presented during lecture hours. • The online teaching tool, myeLearning, will be used for delivery of lectures and lab sessions, official posting of important notices and provision of recommended resource materials.

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Learning outcomes / Competences

- Identify appropriate modelling strategies for a range of real-world systems; - Implement and analyse a model using graphs of functions; - Formulate and analyse models for deterministic processes evolving in discrete time; - Formulate and analyse multi-species population and epidemiological models;

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Forms of examination

Coursework and final examinations will be delivered online via the MyElearning platform and are asynchronous in nature. Take-home assignments will also be provided. The course assessment has three components: • Two coursework exams based on theory - 25% of overall grade; • Five Computer lab practical assignments - 25% of overall grade; • Final exam - 50% of overall grade.

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Conditions for allocation of credit points

Passing total mark (sum of coursework and final examination marks).

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Other information

This course provides students with a platform to develop such modelling skills. It also provides an opportunity for students to develop a capacity for independent thought and critical analysis. As mathematical modelling is extensively utilized in science and engineering research and development, it will be of great benefit not only to applied mathematicians, but also to future researchers in their chosen field of science and technology.