20 credits at level HE4
To introduce learners to a range of core principles and techniques in Mechanical Engineering by the promotion of problem solving skills and methods.
Mathematical methods – Appreciate and use algebra
Transformation of formulae. Solution of basic equations (polynomial order <=2) – factorisation, use of formulae and illustration by graphical means.
To sketch and use graphs – Predict the behaviour of single valued functions.
Linear, Polynomials, Exponential, Non-linear to linear transformations.
To solve problems using trigonometry – Appreciate the use and application of trigonometry
Solution of triangles, Compound angle formula.
Statistical techniques – Appreciate trends and sources of inaccuracies in measured/sampled data.
Binomial expansion, Mean, median and mode, Normal, Poisson and Binomial distributions, Probability and its laws, Regression of correlation.
To learn the basic use of vectors – Promote spatial awareness by standardisation
Concept of a vector – scalar and vector quantities; Vector algebra and resolution of vectors into rectangular co-ordinates, Scalar and vector products. Moment of a force and angular velocity.
Forces and stress – Vector methods to static problems
Co-planar and concurrent forces; Moment of a force and couples. Newton’s Laws. Loading Types: Force, Moments, Torque’s, Traction, Pressure using rods, beams and bars (structural elements). Condition for static equilibrium. Resultants and equilibrium of concurrent and non-concurrent force systems. Simple pin jointed frameworks;
Use of calculus – Appreciate the effect of changing one quantity with respect to another
Concept of differentiation. Differentiation of basic functions. Definitions of linear displacement, velocity and acceleration. Equation of linear motion with constant acceleration. Velocity-time graphs. Definitions of angular displacement, velocity and acceleration. Equations of angular motion with constant acceleration. Relationship between linear and angular motion Numerical differentiation and use of spreadsheets in differentiation.
Integration – Appreciate the effect of reversing the process of differentiation. Used to find areas under curves.
Concept of integration as reverse of differentiation. Integration of basic functions. Definite and indefinite integration. Integration as area under a graph. Numerical integration.
Complex numbers – To extend the simple number system in order to include complex numbers and solve related problems.
Appreciate the concept of a complex number; Notation, Cartesian, polar and exponential forms. Arithmetical operations.
To analyse simple stress and strain concepts – To appreciate the strength of materials and its definition
Direct stress and strain. Hooke’s Law and Young’s Modulus of Elasticity. Tensile strength and factor of safety. Thermal expansion Effects of thermal strain. Shear stress and strain. Modulus of rigidity.
General dynamics – Appreciate the force exerted upon and by moving bodies
Definition of basic dynamic terms and relationships between dynamic characteristics; Definitions of mass, force weight momentum. Newton’s Laws of Motion. Relationship between force and linear acceleration. D’Alembert’s principle and free body diagrams. Relationship between torque and angular acceleration. Moment of Inertia and radius of gyration. Centripetal acceleration. Centripetal and centrifugal forces.
Work and energy – Analyse work and forms of energy with its conservation
Definition of work. Equivalent work/energy. Work done by a force and a torque. Power transmitted by a force and a torque.
Delivery of this module will concentrate on promoting problem solving skills using known and accepted mathematical techniques and scientific principles.
The delivery will be structured as follows:
Formal lectures constitutes to the delivery of the specified curriculum 42
Tutorials and problem solving support in order to reinforce the above delivery 20
Laboratory sessions used to determine the limitations of scientific principles of the
Assignments specific to laboratory sessions 40
Two phase tests in order to assess previous unseen questions that are similar to the
ones illustrated in the problem solving sessions 4
Self directed learning specific to the syllabus content 86
when you have successfully completed this module you will:
to demonstrate that you have achieved the learning outcome you will:
|1.||Analyse specific problems using appropriate analytical techniques
Appreciate the application and limitation of the theory used.
Assess the sensitivity of the obtained results/solutions/
Solve problems associated with Mechanical Science using pre-prepared data and appropriate analytical techniques.
Explain approximations used and its effect e.g. real life measured inertia values compared to mathematically derived values.
Investigate the effect on the solution by changing various parameters and appreciate the general trend e.g. Calculus exact and approximate gradients at various points on a curve.
|2.||Apply different theories presented in this module.
Interpret the problem posed and generate a sequence of tasks necessary to solve the problem.
Demonstrate theoretical knowledge by a laboratory based experiment or case study, based upon measurements and calculations.
Illustrate the general sequence and carry them out e.g. Production of free body diagram and application of Newton’s and D’Alembert’s principle.
|3.||Conduct an experiment in a laboratory environment and be able to manipulate the generated/given data.||Extract and present data in the form of a technical report.|
|4.||To apply mathematical concepts to other situations.||Use mathematical and numerical techniques to solve a range of problems.|
Your achievement of the learning outcomes for this module will be tested as follows:
|Description||Phase tests 1||Phase tests 2|
There are no prerequisites for this module.
No restrictions apply.
Mildren K.W. & Hicks, P.J., - Editors, (1996) Information Sources in Engineering. Bowker-Saur.
Stephens, J. & Hall – Editor, (`1999) Kempe’s Engineers Year Book for 1999. Miller Freeman.
Timings, R.L. (1998) fundamentals of Engineering. Longman.
Tooley, M. & Dingle, L. (1998) Higher National Engineering. Newness.
British Broadcasting Corporation (1995) Longest Bridge. BBC 2
British Broadcasting Corporation (1995) Trickiest Tunnel. BBC 2
British Broadcasting Corporation (1995) Largest Place. BBC 2
James, Glyn (1992) Modern Engineering Mathematics Addison Wesley
Stroud, K. (1995) Engineering Mathematics – MacMillan
Farlow, S. J. Heggard, G. J. (1990) – Introduction to Calculus with Applications, MdGrawhill
Mustoe, L. R. Barry, M. D. J. (1998) Mathematics in Engineering and Science Wiley.
Croft, A. Davison, R. Hargreaves, M. (1995) Engineering Mathematics Addison Wesley.
|Host Subject Group:||Engineering|
|User Name||Date Accessed||Action|