MATH07035 2019 Mathematics 3
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;
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 methods.
Calculate powers of complex numbers using theorems of DeMoivre and Euler.
Solve linear systems using Gaussian Elimination and apply this to engineering problems
Be able to obtain the z-Transform of some standard functions and solve first order difference equations.
Evaluate eigenvalues and eigenvetors and solve matrix transformation problems
Teaching and Learning Strategies
.
Module Assessment Strategies
Written examinations
Moodle quizzes
Repeat Assessments
.
Indicative Syllabus
- First order differential equations: separation of the variables, exact and inexact forms. 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. 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.
- Gaussian Elimination and applications. Determinants and Cramer's rule.
- Eigenvalues and eigenvectors, matrix transformations.
- Z and inverse z transforms. Solution of difference equations by z-transform.
Coursework & Assessment Breakdown
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 |
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
Authors |
Title |
Publishers |
Year |
K.A.Stroud |
Engineering Mathematics |
Palgrave and Macmillan |
2007 |
None
None
None
None