MATH07024 2013 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
2013 - Full Academic Year 2013-14
End Term
2016 - Full Academic Year 2016-17
Author(s)
David Mulligan, Grace Corcoran
Programme Membership
SG_EMECL_B07 201300 Bachelor of Engineering in Mechanical Engineering SG_EMECH_B07 201300 Bachelor of Engineering in Engineering in Mechatronics SG_EMECH_B07 201300 Bachelor of Engineering in Engineering in Mechatronics SG_EMECH_B07 201300 Bachelor of Engineering in Engineering in Mechatronics SG_EPLYP_J07 201300 Bachelor of Engineering in Polymer Processing SG_ETRON_J07 201800 Bachelor of Engineering in Engineering in Electronic Engineering SG_EMECH_B07 201300 Bachelor of Engineering in Mechanical 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.

7.

Evaluate eigenvalues and eigenvetors

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

 

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

End of Semester / Year Assessment

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

Full Time Mode Workload


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

Part Time Mode Workload


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

Online Learning Mode Workload


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

Additional Information

None