Applied Mathematics 2 | Abertay University

Applied Mathematics 2

Description

This module expands on the concepts of Applied Mathematics 1, on applied mathematics relevant to the Computer Games Technology programme.

Aims

The aim of this module is to provide the student with: an appreciation of the advanced 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 calculus methods to describe/approximate surfaces and to solve optimisation problems.

2.  Use the ideas of homogeneous coordinate matrix transformations and quaternions for 3D rotations in computer graphics applications.

3.  Use the rays and beams in the modelling of reflection, refraction and collision detection with regular shapes.

4.  Solve problems in 1D involving variable acceleration and resistance.

5.  Solve problems in 2D, including circular and simple harmonic motion; and elastic collisions.

Indicative Content

1 Calculus

First and second order partial differentiation. Extrema of two variable functions.

2 Matrix and Quaternion Transformations

3D matrix transformations: translation, scaling, rotation and reflection. Parallel and perspective projections. Complex numbers. Quaternions and their application to rotations about an axis.

3 Vector Curves and Surfaces

Vector geometry of curves and surfaces in space. Tangent planes and normals.

4 Ray Tracing

Intersection of rays with 3D surfaces. Tracing reflected and refracted rays of light in 3D using vectors.

5 Dynamics

Variable velocity and acceleration. Straight−line dynamics with variable forces (e.g. dependent on speed). Circular motion, simple harmonic motion. Oblique impact of objects in 2D.

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. The learning outcomes will be assessed 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 60
Independent 92



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 2018/19 , and may be subject to change for future years.