20 credits at level HE5
To develop mathematical analysis skills to a level suitable to be applied to engineering problems
To develop analytical and numerical technique skills as applied to model problems in the engineering environment
To introduce the application of statistical analysis to model problems
To further make use of problem solving software
* Implicit and logarithmic differentiation.
* Partial differentiation including higher order derivatives.
* Total differential and application to small changes and rates of change.
* Maximum/minimum/saddle points for functions of two variables.
2) LINEAR ALGEBRA
* Solution of linear simultaneous equations using Gaussian elimination.
* Eigen values/Eigen vectors and applications.
* Iterative solutions of linear simultaneous equations using Jacobi and Gauss Seidel methods.
3) LAPLACE TRANSFORMS
* Introduction to Laplace transforms and tables of transforms.
* First shift theorem.
* Inverse transforms and tables of inverse transforms.
* Solution of first and second order differential equations.
4) NUMERICAL METHODS
* Numerical solution of differential equations using Euler, Improved Euler and Runge/Kutta methods.
* Development of double integration for three dimensional cases eg. volume integrals.
* Exact differentials.
6) FOURIER SERIES
* Introduction to Fourier series.
* Sinusoidal and non-sinusoidal waveforms.
* Periodic functions in 2pi.
* Fourier coefficients.
* Odd/even functions.
* Fourier sine series, Fourier cosine series.
The delivery of this module will be structured as :
Formal lectures (including lab time and using appropriate software) 2 hrs/wk x 30 wks = 60 hours
Tutorial sessions 1 hr/wk x 30wks = 30 hours
Directed and self learning = 110 hours
Resources: Availability of mathematics and spreadsheet packages such as Derive, Mathcad, Matlab and Excel.
when you have successfully completed this module you will:
to demonstrate that you have achieved the learning outcome you will:
|1.||Mathematically analyse problems||Model a given application example|
|2.||Apply analytical and numerical techniques||Solve relevant engineering problems|
|3.||Apply statistics analysis||Choose, and use appropriately, a suitable statistical analysis|
|4.||Display general IT skills of a professional standard and the ability to use pertinent software for analysis, manipulation and presentation of engineering information||Select and apply appropriate computer based methods for modelling and analysing engineering problems|
Your achievement of the learning outcomes for this module will be tested as follows:
|Description||Problem Solving assignment||Computer Based Analysis assignment||Phase Test||Phase Test|
Before taking this module you must have successfully completed the following:
and/or be taking the following corequisite modules:
You cannot take this module if you are taking or have taken:
Bird and May. Mathematics for Technicians 4/5. (1995) Longmans.
James G., Modern Engineering Mathematics. 3rd Edition (2001) Addison Wesley.
Math Work. Studentís Edition of Matlab 5. (1997) Prentice Hall.
Stroud K., Advanced Engineering Mathematics, 4th Edition, Programmes and Problems. (2003) Macmillan
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