### MA105-4-__ : Applied Mathematics

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.

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 Matlab to assist their investigations, to develop skills in writing laboratory reports and in working with a partner.”