Applied Mathematics - 2025 entry

This module introduces you to mathematical modelling to understand and solve a range of problems concerning real physical systems. You will explore and learn about kinematics of a particle, Newtonian dynamics and its applications. You will also learn about vectors in mechanics and the use of calculus in the modelling of physical systems, as well as how to use theories and mathematical techniques to analyse and reformulate a given problem and communicate results.

Students are expected to have knowledge of Principles of Pure Mathematics as a co-requisite (MTH0001).

One of the main objectives of this module is to develop your ability to use mathematical representations and to recognise their importance for understanding and modelling real-world problems. In which case, a sound foundation of core mathematical machinery is necessary to work out solutions. The module will act as a building block for further advanced studies in mathematics, engineering and applied sciences. The knowledge and skills developed in this module will ease adaptability and engagement with courses in your undergraduate degree programme.

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge

1. Recall and apply mathematical skills to model mechanical and dynamical systems;

2. Formulate models of the physical world, applying mathematical machinery such as vectors and calculus to develop and analyse these models;

3. Present your findings in a logical and coherent manner;

Discipline Specific Skills and Knowledge

4. Formulate and solve problems;

5. Use mathematics as an effective medium of modelling and communication;

Personal and Key Transferable / Employment Skills and Knowledge

6. Learn to analyse and evaluate solutions effectively;

7. Demonstrate self-management and time-management skills.

Topics will include some or all of:

• Elementary vector calculus: vectors and scalars, dot product, cross product, scalar and vector triple product, line, surface and volume integrals

• Elementary ODEs: first-order equations, separable equations and applications, substitution method and exact solutions, second-order linear equations and with constant coefficients, general solutions, nonhomogeneous equations

• Dynamics; Newton’s law

• Forced oscillations and resonance

Deferral – if you have been deferred for any assessment, you will be expected to complete relevant deferred assessments as determined by the Mitigation Committee. The mark given for re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.

Referral – if you have failed the module overall (i.e., a final overall module mark of less than 40%) you will be required to undertake re-assessments as described in the table above for any of the original assessments that you failed. The mark given for a re-assessment taken as a result of referral will be capped at 40%.

Web based and Electronic Resources:

• ELE

Other Resources:

• P.C. Matthews. Vector Calculus, Springer-Verlag (1998)

• C.H. Edwards, D.E. Penney. Differential Equations and Boundary Value Problems, Pearson Education International (2008)

• ‘Guide to Mechanics by Phil Dyke and Roger Whitworth, 2001

• ‘Mechanics’ by W. Chester, 1979

• ‘Particle Mechanics’ by Collinson, C. D. & Roper, T., London: Arnold, 1995

• ‘A first course in mechanics’ by Lunn, M., Oxford: Oxford University Press, 1991

Reading list for this module: