MX34510 - PRINCIPLES OF APPLIED MATHEMATICS

Module Identifier

MX34510

Module Title

PRINCIPLES OF APPLIED MATHEMATICS

Academic Year

2003/2004

Co-ordinator

Dr David M Binding

Semester

Semester 1

Other staff

Dr R S Jones

Pre-Requisite

MA11210

Mutually Exclusive

MA24510

Course delivery

Lecture

19 x 1 hour lectures

Seminars / Tutorials

3 x 1 hour example classes

Assessment

Assessment Type	Assessment Length/Details	Proportion
Semester Exam	2 Hours (written examination)	100%
Supplementary Assessment	2 Hours (written examination)	100%

Learning outcomes

On completion of this module, a student should be able to:

describe the philosophy underlying mathematical modelling;
solve problems involving motion with uniform and variable acceleration;
identify the forces acting on a particle;
determine the motion of a particle by formulating and solving its equations of motion;
apply the principle of work to the solution of problems involving speed and distance;
identify conservation fields of force and derive an equation of energy;
apply the conservation of linear momentum to the solution of problems involving blows and impacts.

Brief description

Applied Mathematics has traditionally involved the study of mathematical models which represent the behaviour and interaction of material objects such as particles, solid objects and fluids in the real world. The main theme of this module is the application of Newton's laws of motion to the motion of particles under various types of forces. This module is self-contained and requires no previous knowledge of mechanics.

Aims

To provide an introduction to basic concepts of traditional applied mathematics. To provide an understanding of Newtonian mechanics.

Content

1. BASIC CONCEPTS: Mathematical Models. Particles, Mass, Rigid Bodies, Length, Time. Units, dimensions.
2. KINEMATICS: Position vector, velocity and acceleration in Cartesian coordinates. Uniform acceleration in a straight line. Simple harmonic motion. Angular velocity. Acceleration of a particle moving in a circle.
3. NEWTONIAN MECHANICS: Momentum, force, laws of motion.
4. PHYSICAL LAWS: Gravitation. Hooke's Law. Friction.
5. PROJECTILE MOTION: One and two dimensional motion of a particle under gravity.
6. WORK, POWER AND ENERGY: Principles of work, conservative forces, conservation of energy.
7. IMPULSE AND IMPACT: Conservation of linear momentum. Inelastic impacts. Impulsive tensions in strings. Impact of elastic bodies.

Reading Lists

Books
** Recommended Text
D Williams (1997) Elements of Mechanics Oxford 0198518811
** Supplementary Text
M Lunn (1991) A First Course in Mechanics Oxford 0198534337
F Chorlton (1983) Textbook of Dynamics 2nd. Ellis Horwood 085312390X
D Humphrey (1930) Intermediate Mechanics Longmans X240088327

Notes

This module is at CQFW Level 6