Module Details

MA105-4-AU-CO: Applied Mathematics

Year: 2017/18
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes
Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No
Outside Option: Yes

Staff
Supervisor: Dr Chris Antonopoulos
Teaching Staff: Dr Chris Antonopoulos, email canton@essex.ac.uk; Mr David Bowers, email dbowers@essex.ac.uk
Contact details: Miss Claire Watts, Department Manager, Tel. 01206 873040, email cmwatts@essex.ac.uk

Module is taught during the following terms
Autumn Spring Summer

Module Description

This course introduces Newtonian Dynamics and develops the application of simple mathematical ideas to study it. The course thereby serves to enhance the skills and knowledge of specialist mathematicians in the second year, in the context of fundamental physical ideas, which have been central both to the development of mathematics over the last three hundred years, to the analysis of aspects of modern technology, and to the understanding of the universe. It provides experience in the use of computer packages, in working together, and in report writing.

Syllabus
- Newton's Laws of Motion.
- Newton's Law of Gravitation. Hooke's law. Friction.
- Newton's Second Law as a differential equation.
- Constant acceleration problems in one, two and three dimensions. Projectiles.
- Simple harmonic motion. Damped simple harmonic motion.
- Definitions of work and energy and their relation to Newton's Laws of Motion.
- Conservative forces; potential energy.
- Conservation of Energy.
- Circular orbits for a single particle in a central field of force.
- Centrifugal force.


Laboratory Programme
1. Projectiles (week 4)
2. Simple Harmonic Motion (week 6)
3. Simple Pendulum (week 7)
4. Ellipses (week 9)
5. Energy (week 11)


On completion of the course students should be able to:
- use vector notation to describe positions in space and their various rates of change;
- state Newton's Laws of Motion;
- state Newton's Law of Gravitation;
- state Hooke's Law of force for a spring;
- apply Newton's Laws and Hooke's Law to the motion of a particle in one dimension;
- recognise the equation of simple harmonic motion and write down its solution;
- analyse the motion of a simple pendulum for small and large displacements;
- be familiar with the concept of friction for bodies at rest and for bodies in motion;
- be able to state and derive the principle of conservation of energy;
- be familiar with the concept of Work;
- analyse the motion of a particle in a constant gravitational field in two dimensions;

An important part of the course is for students to learn how to use a computer package to assist their investigations, and to develop skills in writing laboratory reports, working with a partner.

Learning and Teaching Methods

This course has 2 lectures per week, a one-hour class in weeks 2, 3, 5, 8 and 10 and a two-hour lab in weeks 4,6,7,9,11 throughout the Autumn Term. Three revision lectures are given in the Summer Term. The course has a significant practical component.

Assessment

20 per cent Coursework Mark, 80 per cent Exam Mark

Coursework

Practical work is assessed by means of laboratory reports. Laboratory work is done in teams of two or three. Coursework counts 20% towards the final assessment (4 laboratory reports at 5% each) and the examination counts 80%.

Other details

Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information

Exam Duration and Period

1:30 during Summer Examination period.

Other information

Available to Socrates /IP students spending all relevant terms at Essex.

Bibliography

  • Recommended Reading:
  • For Vectors:
  • E. Kreyszig, Advanced Engineering Mathematics, Wiley
  • For Mechanics:
  • J.M. Knudsen and P.G. Hjorth. Elements of Newtonian Mechanics, 3rd. Edition. Berlin: Springer-Verlag, 2000
  • Supplementary Texts:
  • L.A. Pars Introduction to Dynamics Cambridge
  • P. Smith & R.C. Smith Mechanics Wiley
  • M.R. Spiegel Theory and Problems of Theoretical Mechanics, Schaum

Further information