This module is not currently running in 2024 to 2025.
This module introduces mathematical modelling in a variety of contexts including using Newton's laws of motion, Newton’s law of gravitation, population models, exponential growth, density dependent growth, and predator-prey models. Outline syllabus may include topics from (i) deriving differential equations from data; dimensional analysis; (ii) discrete models and difference equations: steady states and their stability; (iii) continuous models and ordinary differential equations: steady states and their stability; the slope fields and phase lines; (iv) applications of Linear Algebra (in lower dimensions): systems of linear ordinary differential equations; linear phase plane analysis and stability; (v) electrical networks; (vi) vector algebra, vector geometry, vector equations, coordinate systems and vector differentiation; (vii) application in mechanics: Newton's laws for a single particle in 3-D; conserved quantities; angular velocity, angular momentum, moment of a force; harmonic motion.
36 lectures, 12 classes
80% Examination, 20% Coursework
J Berry and K Houston, “Mathematical Modelling: mechanical vibrations, population dynamics, and traffic flow : an introduction to applied mathematics”, Edward Arnold, London, 1995.
D Edwards and M Hamson, “Guide to Mathematical Modelling”, Palgrave, Basingstoke, 1989.
M Lunn, “A First Course in Mechanics”, Oxford University Press, New York, Oxford, 1991.
R K Nagle and E B Saff, “Fundamentals of Differential Equations”, Addison Wesley, 6th Ed., Boston, Mass., London, 2004.
P J Olver and C Shakiban, “Applied Linear Algebra”, Prentice-Hall, Upper Saddle River, NJ, 2006.
P Dyke, R Whitworth, “Guide to mechanics”, Macmillan, Basingstoke, 1992. • P Smith and R Charles, “Mechanics”, Wiley, 2nd Ed., Chichester, 1990.
See the library reading list for this module (Canterbury)
On successful completion of this module students will:
a) have a reasonable knowledge of the various concepts and quantities required in population models and Newtonian mechanics;
b) be aware of how these quantities are linked by equations, using vectors and matrices where appropriate;
c) have a reasonable ability to derive and study these equations and interpret the results in terms of the original concepts;
d) have a reasonable ability to use MAPLE to illustrate the behaviour of population models;
e) appreciate the applications of Linear Algebra in mathematical modelling.
Students who successfully complete this module will have further developed:
a) an analytical approach to solving problems;
b) their ability to communicate solutions, simple proofs and calculations;
c) their numeracy and computational skills;
d) their ability to plan and carry out effective ways of studying.
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