Pre-requisite: MAST4006 (Mathematical Methods 1)
OverviewThis module introduces mathematical modelling and Newtonian mechanics. Tutorials and Maple worksheets will be used to support taught material.
The modelling cycle: General description with examples; Newton's law of cooling; population growth (Malthusian and logistic models); simple reaction kinetics (unimolecular and bimolecular reactions); dimensional consistency
Motion of a body: frames of reference; a particle's position vector and its time derivatives (velocity and acceleration) in Cartesian coordinates; mass, momentum and centre of mass; Newton's laws of motion; linear springs; gravitational acceleration and the pendulum; projectile motion
Orbital motion: Newton's law of gravitation; position, velocity and acceleration in plane polar coordinates; planetary motion and Kepler's laws.
This module appears in:
Method of assessment
80% examination and 20% coursework.
C. D. Collinson and T. Roper, Particle Mechanics, Butterworth-Heinemann, 1995
J. Berry and K. Houston, Mathematical Modelling, Butterworth-Heinemann, 1995
On successfully completing the module students will be able to:
1 demonstrate knowledge of the underlying concepts and principles associated with simple ODE-based mathematical models;
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts in the following areas, whilst demonstrating a reasonable level of skill in calculation and manipulation of the material: the modelling cycle, simple models of growth and decay processes, basic Newtonian mechanics, orbital motion;
3 apply the underlying concepts and principles associated with mathematical modelling in several well-defined contexts, showing an ability to evaluate the appropriateness of different approaches to solving problems in this area;
4 make appropriate use of Maple.
The intended generic learning outcomes.
On successfully completing the module students will be able to demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle) and Maple;
7 communicate technical and non-technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.