MATH08013 2019 Mathematics 4
Level 8 Mathematics for 4th year classes in Mechatronics, Mechanical and Electronic Engineering
Learning Outcomes
On completion of this module the learner will/should be able to;
Use Taylor's series to approximate transcendental functions
Use Fourier series to approximate periodic functions
Calculate Discrete Fourier Transforms and inverse Discrete Fourier transforms of signals
Solve first and second order difference equations using z-transforms
Demonstrate an understanding of the concepts of vector space, dimension, rank, linear independence and spanning sets
Solve geometrical problems using the i, j, k orthogonal triad system, and compute dot products and cross products. Compute projections and angles between vectors and interpret results geometrically
Use first and second order differential and difference equations and linear algebra to model and solve engineering problems
Teaching and Learning Strategies
Lectures and tutorials
Module Assessment Strategies
CA and final examination
Repeat Assessments
Repeat final examination
Indicative Syllabus
1. Taylor's series and Taylor polynomials. Approximating transcendental functions in a neighbourhood of a point.
2. Even and odd functions, real Fourier series and complex Fourier series.
3. Complex roots of unity, Discrete Fourier Transforms and Inverse Discrete Fourier Transforms as symmetric linear transformations.
4. Sequences, sampling of functions, first and second order difference equations. Definition and properties of the z-transform. Inverse z-transform and left shift theorems. Solution of first and second order difference equations using z-transforms.
5. Introduction to abstract vectors as matrices. Linear independence (using Gaussian elimination), spanning sets, vector spaces, dimension and rank.
6. Vector geometry of 2, 3 and higher dimensions. The i, j, k orthogonal triad system, computation of dot products and cross products. Computation of projections and angles between vectors and interpretation of results geometrically.
7. Application of difference equations and linear algebra to model and solve engineering applications.
Coursework & Assessment Breakdown
Coursework Assessment
Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
---|---|---|---|---|---|---|
1 | Continuous Assessment Continious Assesment | 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 | Closed Book Exam | 70 % | End of Term | 1,2,3,4,5,6,7 |
Full Time Mode Workload
Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|
Tutorial | Flat Classroom | Tutorial | 1 | Weekly | 1.00 |
Lecture | Tiered Classroom | Theory | 2 | Weekly | 2.00 |
Independent Learning | Not Specified | Independent Learning | 4 | Weekly | 4.00 |
Part Time Mode Workload
Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|
Lecture | Distance Learning Suite | Lecture | 2 | Weekly | 2.00 |
Tutorial | Distance Learning Suite | Tutorial | 1 | Weekly | 1.00 |
Independent Learning | Not Specified | Independent Learning | 4 | Weekly | 4.00 |
Module Resources
Authors |
Title |
Publishers |
Year |
K.A.Stroud |
Engineering Mathematics |
Palgrave and Macmillan |
2007 |
None
None
Khan Academy
None