SCQF Level: 07
Module Code: MAT101
Credit Value: 20
Term: Term 1
School: School of Arts, Media and Games
This module covers the basic concepts of applied mathematics relevant to the Computer Games Technology programme.
The aim of this module is to provide the student with: the basic ideas and techniques in applied mathematics relevant to Computer Games Technology.
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. Solve problems in plane geometry involving lines, circles and the conic sections.
3. Apply matrix transformations and vector methods for use in 2− and 3−dimensional space.
4. Apply the equations of kinematics and Newtonian concepts involving momentum, impulse and energy to formulate and solve the resulting models.
Basic function definitions, composition, inverse; polynomial, rational, exponential, logarithmic and trigonometric functions. Graphs of functions. Appreciation of need to approximate functions in some applications and for careful evaluation on computers − errors.
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.
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. There will be a formative test during structured feedback week. Assessment will be by a practical portfolio of applications of mathematics in Matlab, and by an end of semester exam.
Teaching and Learning Work Loads
|Supervised Practical Activity||12|
|Unsupervised Practical Activity||0|
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.