# Applied Mathematics 1

## Description

This module covers the basic concepts of applied mathematics relevant to the Computer Games Technology programme.

## Aims

The aim of this module is to provide the student with: the basic ideas and techniques in applied mathematics relevant to Computer Games Technology.

## Learning Outcomes

By the end of this module the student should be able to:

1.  Use standard functions and approximations to solve problems involving rates of change by calculus methods.

2.  Apply matrix transformations and vector methods for use in 2- and 3- dimensional space.

3.  Apply the basic kinematics equations to solve problems in dynamics.

4.  Apply Newtonian concepts involving forces, momentum, impulse and energy to formulate and solve resulting models.

## Indicative Content

### 2 Calculus

Rates of change, derivatives of standard functions. Rules for derivatives of sums, products, quotients and composite functions. Higher derivatives and applications. Indefinite and definite integrals − integration methods. Application to areas, mean values, etc.

### 3 Geometry

Plane coordinate geometry of lines, circles and conic sections. Vectors in 2 and 3 dimensions, scalar and vector products − use in projection and 3D geometry.

### 4 Matrices and Transformations

Basic matrix operations, determinants, inverses. Solving linear equations by matrix inverse. Matrix transformations of the plane − translations, scalings, rotations and reflections. Homogeneous coordinates.

### 5 Kinematics in a straight line

Newton's laws of motion. Momentum and impulse, collision of bodies (1−dimensional, elastic and inelastic). Kinetic and potential energy, elastic strings. Work and Power. Coplanar forces. Friction.

## Statement on Teaching, Learning and Assessment

The module will be delivered by a mixture of lectures and tutorials. Assessment will be by a Portfolio of analytical problem solving, and by an end of semester exam.

## Teaching and Learning Work Loads

 Total 200 Lecture 24 Tutorial/Seminar 24 Supervised Practical Activity 0 Unsupervised Practical Activity 0 Assessment 80 Independent 72

## Guidance notes

Credit Value – The total value of SCQF credits for the module. 20 credits are the equivalent of 10 ECTS credits. A full-time student should normally register for 60 SCQF credits per semester.

## Disclaimer

We make every effort to ensure that the information on our website is accurate but it is possible that some changes may occur prior to the academic year of entry. The modules listed in this catalogue are offered subject to availability during academic year 2019/10 , and may be subject to change for future years.