Module Identifier MX34510 Module Title PRINCIPLES OF APPLIED MATHEMATICS Academic Year 2001/2002 Co-ordinator Professor T Phillips Semester Semester 1 Other staff Professor Arthur Davies, Dr R Jones Pre-Requisite MA11210 Mutually Exclusive MA24510 Course delivery Lecture 19 x 1 hour lectures Seminars / Tutorials 3 x 1 hour example classes Assessment Exam 2 Hours (written examination) 100% Resit assessment 2 Hours (written examination) 100%

#### General 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.

#### 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.

#### Syllabus

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.