# MATH07008 2009 Mathematics

### General Details

Full Title
Mathematics
Transcript Title
Maths
Code
MATH07008
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
2009 - Full Academic Year 2009-10
End Term
9999 - The End of Time
Author(s)
Joe Gildea
Programme Membership
SG_EMOBI_B07 201300 Bachelor of Engineering in Mobile communications SG_EELEC_B07 201100 Bachelor of Engineering in Electronic Engineering SG_EELEC_J07 200900 Bachelor of Engineering in Electronic Engineering
Description

This module consists of topics from Intergal and Differential Calculus, Linear Algebra and Complex Numbers. These topics include differental 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

4.

Calculate powers of complex numbers using theorems of DeMoivre and Euler and calculate the Fourier transform of functions

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.

### Indicative Syllabus

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.

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.

The homogeneous equation .  Solution of the non-homogeneous equation   using the complementary function and particular integral.

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.

Gaussian Elemination and applications.

### 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 Continuous Assessment Continuous Assessment UNKNOWN 30 % OnGoing 1,2,3,4,5,6

### End of Semester / Year Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 Final Exam Final Exam UNKNOWN 70 % End of Year 1,2,3,4,5,6

Type Location Description Hours Frequency Avg Workload
Lecture Lecture Theatre Theory 2 Weekly 2.00
Tutorial Lecture Theatre Tutorial 1 Weekly 1.00
Independent Learning UNKNOWN Self Study 1 Weekly 1.00
Total Full Time Average Weekly Learner Contact Time 3.00 Hours

Type Location Description Hours Frequency Avg Workload
Lecture Not Specified Lecture 1 Weekly 1.00
Tutorial Not Specified Tutorial 1 Weekly 1.00
Directed Learning Not Specified Conitnuous Assessment quizzes / problems 3 Weekly 3.00
Total Part Time Average Weekly Learner Contact Time 5.00 Hours

### Module Resources

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

None