# Module Directory

## MA105-4-SP-CO:Applied Mathematics

The details
2019/20
Mathematical Sciences
Colchester Campus
Spring
Current
Monday 13 January 2020
Friday 20 March 2020
15
01 October 2019

Requisites for this module
(none)
(none)
(none)
(none)

MA222, MA225

## Key module for

BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

## Module description

This module introduces Newtonian Dynamics and develops the application of simple mathematical ideas to study it.

## Module aims

This module 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.

## Module learning outcomes

On completion of this module 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; 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.

## Module information

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.

An important part of this module 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.

## Learning and teaching methods

This module has a two-hour lecture each week, a one-hour class each week and five hours of labs throughout the term. Three revision lectures are given in the Summer term. The course has a significant practical component.

## Bibliography

This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   Lab Report 1    0%
Coursework   Lab Report 2    50%
Coursework   Lab Report 3    0%
Coursework   Lab Report 4    50%
Exam  1440 minutes during Summer (Main Period) (Main)

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr David Penman, email: dbpenman@essex.ac.uk.
Dr David Penman
Dr David Penman (dbpenman@essex.ac.uk)

Availability
Yes
No
No

## External examiner

No external examiner information available for this module.
Resources
Available via Moodle
Of 35 hours, 35 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information
Mathematical Sciences

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