Mathematics for Computer Games 1

This module teaches students some maths

Aims of Module

1. To provide the underpinning fundamental mathematics necessary for computer games software.
2. To provide the elements of 2-d particle dynamics necessary to model dynamical problems related to computer games.

Learning Outcomes

The student will be able to:

1. Solve problems related to elementary trigonometry, coordinate geometry and complex numbers.
2. Differentiate and integrate functions of a single variable and apply to such problems as maxima/minima and area under a curve.
3. Solve simple first and second order differential equations by direct integration and separation of variables.
4. Manipulate (2x2) and (3x3) matrices and determinants, including transformation matrices.
5. Solve simple 2-d dynamical problems using Newton’s Laws.

Outline Syllabus

• Trigonometry: review including trigonometric functions, sine and cosine rules.Coordinate geometry: straight line, circle, quadratic and cubic functions, distance between two points, intersections. Complex Numbers: algebraic form, Argand Diagram, polar and exponential forms.(20%)
• Matrices: manipulation of (2x2) and (3x3) matrices and determinants, inverse, rotation matrices. Vectors: Cartesian form, scalar and vector products, distance between points and angles between vectors, translation of points.(20%)
• Calculus: differentiation and integration, maxima and minima, area under a curve, Maclaurin series, solution of first and second order ordinary differential equations by direct integration and separation of variables.(20%)
• Particle Dynamics (2-d): Newton’s Laws, models of forces, motion under constant acceleration including projectile motion, impact, case studies.(40%)