This module has two aims:
1. to introduce basic matrix techniques for the formulation and solution of engineering problems. These techniques include the representation of geometric transformations, the power method to find eigenvalues and the solution of systems of differential equations.
2. to use partial differentiation to formulate and solve optimisation problems in several variables and to perform error analysis.

Learning Outcomes

On successful completion of this module the learner will be able to:

LO1

Use matrices to construct and analyse geometric
transformations in 2D

LO2

Find the eigenvalues of a 2 by 2 matrix and apply to diagonalisation and power of a matrix

LO3

Find the largest and smallest eigenvalue of a matrix using the Power Method

LO4

Solve a system of first order
differential equations (homogeneous and none homogeneous) with constant coefficients
(2D) using matrix techniques both analytically and numerically (Euler Method).

LO5

Convert a higher order DE into a system of first
order DE’s

LO6

Use matrix techniques to find the normal modes and frequencies of undamped coupled oscillators

LO7

Calculate partial derivatives of polynomials to solve max/min problems in 2D and do error analysis

Module Content & Assessment

Course Work

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Continuous Assessment

CA Test covering Linear Transformations and coupled first order differential equations

1,2,3,4

10.00

Week 7

Continuous Assessment

High threshold Keyskills test in lab

1,2,3,4,5,6,7

10.00

Week 11

Assignment

Implement the Power Method and Euler's Method in the lab

3,4

10.00

Week 7

End of Module Formal Examination

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Formal Exam

End-of-Semester Final Examination

1,2,3,4,5,6,7

70.00

End-of-Semester

TU Dublin – Tallaght Campus reserves the right to alter the nature and timings of assessment

Module Workload

Workload: Full Time

Workload Type

Workload Description

Hours

Frequency

Average Weekly Learner Workload

Lecture

Classwork

3.00

Every Week

3.00

Independent Learning Time

Outside of Class

4.00

Every Week

4.00

Lecturer/Lab

Session in Computing Laboratory

1.00

Every Week

1.00

Total Weekly Learner Workload

8.00

Total Weekly Contact Hours

4.00

This module has no Part Time workload.

Module Resources

Recommended Book Resources

K. A. Stroud,Dexter J. Booth, Engineering Mathematics, 4th ed Ed. [ISBN: 9780831133276]

K. A. Stroud,Dexter J. Booth, Advanced Engineering Mathematics, 4th ed Ed., Palgrave MacMillan [ISBN: 9781403903129]

Michael E. Mortenson, Geometric Transformations for 3D Modeling [ISBN: 9780831133382]

This module does not have any article/paper resources