# MATH07035 2019 Mathematics 3

### General Details

Full Title
Mathematics 3
Transcript Title
Mathematics 3
Code
MATH07035
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
2019 - Full Academic Year 2019-20
End Term
9999 - The End of Time
Author(s)
Kevin Collins
Programme Membership
SG_EELCO_B07 201900 Bachelor of Engineering in Engineering in Electronic and Computing SG_EMECL_B07 201900 Bachelor of Engineering in Mechanical Engineering SG_EPREC_B07 201900 Bachelor of Engineering in Precision Engineering and Design SG_EMTRN_B07 201900 Bachelor of Engineering in Mechatronic Engineering SG_EMTRN_J07 201900 Bachelor of Engineering in Mechatronic Engineering SG_EPREC_J07 201900 Bachelor of Engineering in Precision Engineering and Design SG_ETRON_J07 201900 Bachelor of Engineering in Electronic and Computer Engineering SG_EPLYP_J07 201900 Bachelor of Engineering in Engineering in Polymer Processing SG_EMTRN_J07 202000 Bachelor of Engineering in Mechatronic Engineering SG_EMSYS_B07 201900 Bachelor of Engineering in Mechatronic Systems SG_EMECH_N07 202000 Minor Award in Mechatronic Engineering SG_EMECH_H08 202100 Bachelor of Engineering (Honours) in Mechatronic Systems SG_EPOLP_J07 202200 Bachelor of Engineering in Polymer Process Engineering SG_ETRON_J07 202200 Bachelor of Engineering in Electronic and Computer Engineering SG_EELCO_B07 202200 Bachelor of Engineering in Engineering in Electronic and Computing
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 Elimination 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 Elimination 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

.

### Module Assessment Strategies

Written examinations

Moodle quizzes

.

### Indicative Syllabus

1. First order differential equations: separation of the variables, exact and inexact forms. 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.   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.
5. Gaussian Elimination and applications. Determinants and Cramer's rule.
6. Eigenvalues and eigenvectors, matrix transformations.
7. Z and inverse z transforms. Solution of difference equations by z-transform.

### 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 Semester 1 Exam Final Exam Closed Book Exam 35 % End of Semester 1,2,3
2 Semester 2 Exam Final Exam Assessment 35 % End of Semester 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

### Required & Recommended Book List

1982-07-08 Engineering Mathematics: Programmes and Problems Macmillan
ISBN 0333340523 ISBN-13 9780333340523
2017-05-25 Engineering Mathematics Routledge
ISBN 9781138673595 ISBN-13 9781138673595

### Module Resources

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

None

URL Resources

None

Other Resources

None