# MATH07024 2016 Mathematics 3

### General Details

Full Title
Mathematics 3
Transcript Title
Mathematics
Code
MATH07024
Attendance
N/A %
Subject Area
MATH - Mathematics
Department
MENG - Mech. and Electronic Eng.
Level
07 - NFQ Level 7
Credit
05 - 05 Credits
Duration
Stage
Fee
Start Term
2016 - Full Academic Year 2016-17
End Term
9999 - The End of Time
Author(s)
David Mulligan, Kevin Collins
Programme Membership
SG_ETRON_B07 201600 Bachelor of Engineering in Electronic Engineering SG_EMECL_B07 201600 Bachelor of Engineering in Mechanical Engineering SG_EMECH_B07 201700 Bachelor of Engineering in Engineering Mechatronics Systems Engineering SG_EELCO_B07 201700 Bachelor of Engineering in Electronic and Computer Engineering SG_EELCO_B07 201800 Bachelor of Engineering in Electronic and Computer Engineering SG_EDATA_J07 201900 Bachelor of Engineering in Engineering in Data Centre Facilities Engineering
Description

This module consists of topics from Integral and Differential Calculus, Linear Algebra and Complex Numbers. These topics include differential equations and applications, Laplace Transforms, De Moivre's Theorem, Fourier Transforms, Gaussian Elemination and z-transforms.

### Learning Outcomes

On completion of this module the learner will/should be able to;

1.

Solve first order differential equations using separable variables technique and the integrating factor method

2.

Solve first and second order differential equations using Laplace transforms

3.

Solve second order differential equations using the complementary function and particular integral methods.

4.

Calculate powers of complex numbers using theorems of DeMoivre and Euler.

5.

Solve linear systems using Gaussian Elemination and apply this to engineering problems

6.

Be able to obtain the z-Transform of some standard functions and solve first order difference equations.

7.

Evaluate eigenvalues and eigenvetors and solve matrix transformation problems

.

.

.

### Indicative Syllabus

1. First order differential equations: separation of the variables, exact and inexact forms. Solution of homogeneous differential equations (use of the substitution y= vx )Solution of linear differential equations  using the Integrating Factor Method.
2. Definition of Laplace transform and calculation of the Laplace transform and inverse Laplace transform of functions.  First Shifting Theorem and Laplace transform of derivatives.  Solution of first and second order differential equations using Laplace transforms.
3. The homogeneous equation .  Solution of the non-homogeneous equation   using the complementary function and particular integral.
4. DeMoivre's Theorem and Euler's Theorem for the polar form of a complex number.  Argand diagrams and powers of complex numbers.  Fourier transform of functions.
5. Gaussian Elemination and applications.
6. Eigenvalues and eigenvectors, matrix transformations.

### Coursework & Assessment Breakdown

Coursework & Continuous Assessment
30 %
End of Semester / Year Formal Exam
70 %

### Coursework Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 CA 15% Semester 1, 15% Semester 2 Continuous Assessment Assessment 30 % OnGoing 1,2,3,4,5,6,7

### End of Semester / Year Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 FE 35% Semester 2, 35% Semester 2 Final Exam Assessment 70 % End of Year 1,2,3,4,5,6,7

Type Location Description Hours Frequency Avg Workload
Lecture Lecture Theatre lecture 2 Weekly 2.00
Tutorial Computer Laboratory Tutorial 1 Weekly 1.00
Independent Learning Not Specified Independent Learning 3 Weekly 3.00
Total Full Time Average Weekly Learner Contact Time 3.00 Hours

Type Location Description Hours Frequency Avg Workload
Lecture Not Specified Independent Learning 4 Weekly 4.00
Total Part Time Average Weekly Learner Contact Time 4.00 Hours

Type Location Description Hours Frequency Avg Workload
Lecture Distance Learning Suite Lecture 2 Weekly 2.00
Total Online Learning Average Weekly Learner Contact Time 2.00 Hours

### Module Resources

Non ISBN Literary Resources
 Authors Title Publishers Year K.A.Stroud Engineering Mathematics Palgrave and Macmillan 2007
Other Resources

None