CERTIFICATE IN MATHEMATICS AND PHYSICS FOR GAMES

Course Modules

Certificate in Mathematics and Physics for Games has been introduce to bridge the gap required for MAGES Advance Diploma – Game Design students to take the study path for BSc in Computer Games Development year 3 of Institute of Technology Carlow, Ireland. The certificate course will cover these topics namely Basic Mechanics, Basic Calculus, Integration and Differential Equations.

Module Description:

Mathematics and Physics for Games
Course length: 90 hours              
Credit: 100
Year:  2012 - 2013

In presenting this module the objective is to build simple mathematical models that describe the behavior of real-life situations. This mathematical description is called a mathematical model. Computer games have become more sophisticated as they attempt to emulate reality more accurately. As a consequence programmers need to be trained in Physics and Mathematics.

Physics is a vast field of science that covers many different, but related subjects. The subject most applicable to realistic game development is the subject of Mechanics. In presenting the basic laws of mechanics we are forming the basis of mathematical modeling. The requirement from Mathematics is knowledge of basic Calculus. In order to describe anything that moves or changes with time, the process of differentiation is the method that is usually used. This is a mathematical concept that was developed by Isaac Newton in the 17th century and is still used today to successfully predict the fight of aircraft, projectiles, the planets, etc. Computer games that simulate football, car racing, airplanes in fight or indeed any object that moves or changes with time, will need the ideas of differentiation, if they are to appear realistic.

To construct a mathematical model we first identify the variables that are responsible for changing the system (we may choose not to involve all these variables into the model at first). Secondly we make a set of reasonable assumptions about the system we are trying to describe which will include any laws that may be applicable to the system. For our purposes it will be sufficient to consider simple real-life problems with few variables. For example, when studying mechanics problems we will ignore the retarding force of air resistance in modeling the motion of a body falling near the surface of the earth, but if you are a scientist whose job it is to accurately predict the flight path of a long range projectile, you have to take into account air resistance and other factors such as the curvature of the earth. Since the assumptions made about a system frequently involve a rate of change of one or more variables, the mathematical depiction of all these assumptions may be one or more equations involving derivatives. In other words, the mathematical model may be a differential equation or a system of differential equations.

Once we have formulated a mathematical model (differential equation) we must try to solve it using our knowledge of basic calculus (explicit solution). If we can solve it, then we deem the model to be reasonable if its solution is consistent with either experimental data of known facts about the behavior of the system. But if the predictions produced by the solution are poor, we can either increase the number of variables or change the assumptions to improve the model.

Increasing the number of variables will increase the complexity of the mathematical model and increase the likelihood that we cannot obtain an explicit solution. Hence it is necessary to have methods for approximating the solution. The first numerical method of solution to a differential equation we will consider is Euler's method. This method serves to illustrate the concepts involved in more advanced methods. It has limited usage because of the large error that is accumulated as the process proceeds. We will consider other numerical methods of solution to a differential equation, notably the Runge-Kutta method, which will provide a more accurate solution.

In summary, this subject will be presented as follows: Basic Mechanics, Basic Calculus, Differential Equations and Basic Mathematical Modeling.