20 credits at level HE4
1. To apply a range of mathematical techniques and select an appropriate technique for
solving a given mathematical problem whilst having an appreciation of the need for accuracy in
solving mathematical problems.
2. To select an appropriate technique for solving a given mathematical problem
3. To introduce the application of statistical analysis to model problems
4. To display general IT and mathematical skills of a professional standard and the ability to use pertinent software for analysis, manipulation and presentation of engineering information making use of appropriate software.
Review of algebraic skills and manipulation, transposition of formulae, factorisation of algebraic expressions, solution of equations including simultaneous and quadratic equations.
Use of trigonometric functions and inverse trigonometric functions. Trigonometric identities and the solution of trigonometric equations.
Vector Algebra and Complex Numbers
Vector representation, Vector algebra vector addition and subtraction. Argand diagram. Cartesian and Polar forms of complex numbers. Euler Notation and De Moivre's Theorem
Differentiation: Rate of change of a one-variable function. Differentiation of elementary functions (polynomial, trigonometric, log/exponential etc). Product, quotient and function of a function rules. Use of logarithms in differentiation. Implicit differentiation. Parametric form of a function and differentiation. Chain rule. Higher order derivatives.
Maxima and minima of functions (stationary points) and applied problems.
Integration: Reverse process of Differentiation. Visualization as area under curve. Indefinite and definite integrals using elementary functions (polynomial, trigonometric, log/exponential etc). Integration by parts.
Differential Equations: Modelling using simple circuit examples of first and second order system. Solution techniques using variable separation and exponention forms. Complementary Functions & Particular Integrals. Initial/Boundary conditions.
Basic matrix algebra. Properties and numbers associated with a matrix such as determinant, rank. Special matrices - Null, Identity, transpose, adjoint, inverse, symmetric, diagonal, skew etc.
Solution of systems of linear equations.
Transformations (translation, rotation & deformation) of 2D & 3D objects.
Data Analysis & Numerical Methods
Histograms and Cum. Freq. , Averages , Measures of Dispersion
Stem and Leaf, Box and Whisker Diagrams, Five Point Summary, Skewness
Regression ( Linear & Non-Linear), Product Moment Correlation Coefficient, Correlation
Discrete Random Variables, Expectation and Variance
Probability Distribution Functions, continuous & discrete
Uniform Distribution, The Normal Distribution, The Binomial Distribution, The Poisson Distribution, Normal Approximations
Sampling, Hypothesis Testing , One and Two Tailed Tests, Estimatiors, Central Limit Theorem , Confidence Intervals, Permutations and Combinations, Probability
Technical detail will be introduced to the student by both lectures & practical demonstration. Both delivery mechansms will be supported by student orientated learning exercises, both theoretical & practical.
Both mechanisms will require library & Internet resources to be researched & utilized where appropriate.
when you have successfully completed this module you will:
to demonstrate that you have achieved the learning outcome you will:
|1.||To familiarize with appropriate industry standard design & analysis software.||To select and utilise the most appropriate software tools to solve appropriate analytical problems.|
|2.||To familiarize with the appropriate mathematical techniques necessary to solve the theoretical engineering system models.||To select and use use appropriate analytical mathemeticaltechniques to assist solving theorectical engineering problems.|
|3.||To 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||Computer based written questions to be compled using math software in a time limited exercise||A written time limited test in an exam format||Computer based written questions to be compled using math software in a time limited exercise||A written time limited test in an exam format|
There are no prerequisites for this module.
No restrictions apply.
A Croft, R Davison, Mathematics for Engineers, Addison Wesley 1998.
G James, Modern Engineering Mathematics, 1992.
K A Stroud, Engineering Mathematics, Programmes and Problems, 1993.
L Mustoe Foundation Mathematics, Wiley 1998
L Mustoe Mathematics in Engineering and Science, Wiley 1998
John Rafter, Statistics with Maple, Elsevier Science 2003
Douglas B. Meade, Michael May, S.J., C-K. Cheung, G. E. Keough:- Getting Started with Maple (ISBN 978-0-470-45554-8)
|Host Subject Group:||Electronics|
|User Name||Date Accessed||Action|