Next: MC382 Abstract Algebra
Up: Year 3
Previous: MC380 Ordinary Differential Equations
MC381 Modelling physical systems
| Credits: 20 |
Convenor: Dr. M. D. Dampier |
Semester: 1 |
| Prerequisites: |
essential: MC224, MC225 |
|
| Assessment: |
Regular coursework: 10% |
Three hour exam: 90% |
| Lectures: |
36 |
Classes: |
10 |
| Tutorials: |
none |
Private Study: |
104 |
| Labs: |
none |
Seminars: |
none |
| Project: |
none |
Other: |
none |
| Total: |
150 |
|
|
Course Description
This course presents a variety of examples of the mathematical treatment of the physical
world illustrating the two fundamental approaches to modelling physical systems: the
many-particle model and the continuous medium model. Although the topics to be
considered cannot be treated extensively in the time available, we will in all cases
introduce the fundamental principles upon which deeper study is based. We restrict
ourselves, however, to situations where classical mechanics is applicable.
Aims
This course aims to show the student something of the range of classical applied
mathematics by moving from familiar areas of particle dynamics into an introduction to the
mechanics of fluids. It is intended to make a contribution to the student's general
appreciation of the power of their subject as well as preparing for more advanced courses.
The level 4 course on Partial Differential Equations takes up some of the topics touched
on in this module.
Objectives
At the end of the course students will be able to use dimensional methods to make a first
guess at the likely solution of a problem and to simplify the detailed equations; to handle
classical conservation laws both in few- and many-body problems; to use vector analysis
to obtain the equations of motion of a fluid and some of their simpler implications; and to
apply the theories studied to the solution of a variety of problems.
Syllabus
1. Dimensional invariance
2. The two-body problem in Newtonian gravitational theory
3. Systems of particles
4. The swinging rod
5. Stellar systems
6. Pressure in a fluid
7. Atmospheric pressure
8. Stellar structure
9. Fluid flow - principles and one-dimensional examples
10. Sound waves and shock waves
Transferable Skills
Ability to use classical mechanics to model particular
systems and phenomena.
Ability to use dimensional considerations to guide problem solving.
Experience with SI units.
Problem solving skills.
Reading list
Background:
Because of the variety of topics treated no single book covers all the course material.
References to appropriate reading material are given during the lectures,
Details of Assessment
The final assessment of this module will be based on contributions of 10% from
coursework and 90% from a three-hour examination during the January exam period.
The 10% coursework contribution will come from the weekly work. In all there
will be eight pieces of coursework, the best six being counted.
The examination paper will contain 8 questions, with full marks on the paper
obtainable from 5 complete answers.
Next: MC382 Abstract Algebra
Up: Year 3
Previous: MC380 Ordinary Differential Equations
S. J. Ambler
11/20/1999