MATH07008 2009 Mathematics
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;
Solve first order differential equations using separable variables technique and the integrating factor method
Solve first and second order differential equations using Laplace transforms
Solve second order differential equations using the complementary function and particular integral
Calculate powers of complex numbers using theorems of DeMoivre and Euler and calculate the Fourier transform of functions
Solve linear systems using Gaussian Elemination and apply this to engineering problems
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 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 |
Full Time Mode Workload
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 |
Part Time Mode Workload
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 |
Module Resources
Authors |
Title |
Publishers |
Year |
K.A.Stroud |
Engineering Mathematics |
Palgrave and Macmillan |
2007 |
None