Applied Mathematics - 2022 entry

This module will introduce you to the mathematical techniques used to analyse and to understand a range of problems concerning real physical systems. You will learn how to restructure physical and natural phenomena and model them using mathematical representations which will help us understand the world around us. You will explore and learn about kinematics of a particle moving in a straight line or a plane, the Newtonian dynamics and its applications. Even further, the module uncovers other aspects of dynamics, such as the study of elastic strings and springs, as well as circular motions (horizontal and vertical) and centres of mass. You will also learn about vectors in mechanics and the use of calculus in the modelling of physical systems. 

 

The module will develop your research and communication skills; you will work on small projects individually and as part of a team to formulate and produce justified solutions for models from the physical world; As part of your project output, you will have to demonstrate a coherent and rigorous understanding of the mathematical theories and machinery used.

 

This module will run over two terms; each term you will have weekly scheduled sessions led by the module instructor/convenor. During those sessions you will be introduced to the topic through lecture presentations, learning materials, worked examples and provided exercise worksheet. In this module you will learn how to: use theories and mathematical techniques; analyse and reformulate a given problem; use applied mathematics to investigate natural and physical behaviour; model and communicate results. This will be achieved by encouraging you to develop solutions for the weekly formative exercises in the class while working in small groups. You will be assessed through a combination of summative assessments: in-class tests (2 tests each term), a group mini-project, and a final exam.

 

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.

 

Module Specific Skills and Knowledge:

1 Recall and apply basic techniques in classical mechanics to model simple mechanical and dynamical system

2 Extend the range of mathematical skills to use them in unstructured problems,

3 formulate models of the physical world, applying mathematical machinery such as vectors and calculus to develop and analyse these models;

4 Present your findings in a logical and coherent manner;

 

Discipline Specific Skills and Knowledge:

5 Formulate and solve problems;

6 Demonstrate the ability to recognise when a situation can be represented mathematically and how it is related to a real-world problems 

7 Use mathematics as an effective medium of modelling and communication

 

Personal and Key Transferable/ Employment Skills and Knowledge:

8 Work effectively as part of a small team, and learn to analyse and evaluate solutions;

9 Communicate orally with team members and via written presentation

10 Demonstrate self-management and time management skills.

 

- Two dimensional vectors and vector algebra with applications. 

- Kinematics of a particle moving in a straight line – motion in a horizontal plane with constant acceleration.

- Dynamics of a particle moving in a straight line or plane and applications/Newton’s law

- Statics of a particle and applications of the conditions for equilibrium cases to systems. 

- Kinematics of a particle moving in a straight line or plane - motion in a vertical plane with constant acceleration. 

- Centres of mass of a discrete mass distribution in one or two dimensions; centre of mass of uniform plane figures, and composite plane figures; cases of equilibrium of a plane lamina. 

- Statics of rigid bodies: Equilibrium of rigid bodies involving parallel and non-parallel coplanar forces; 

- Elastic strings and springs - Hook’s Law, equilibria and oscillations; energy stored in an elastic string or spring using work-energy principle with kinetic, gravitational potential energy and elastic potential energy 

- Simple harmonic motion, e.g. simple pendulum 

- Motion in a circle - motion in a horizontal circle; motion of a particle in a vertical circle   

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%.

Basic reading/Web-based and electronic resources: 

 

• ELE – College to provide hyperlink to appropriate pages