Department of Mechanical Engineering, Unit Catalogue 2010/11 |
ME10305: Mathematics 2 |
 Credits:
| 6 |
| Level:
| Certificate |
| Period: | This unit is available in... |
| Semester 2 |
| Assessment:
| EX 100% |
| Supplementary Assessment: | ME10305 Re-assessment Examination (where allowed by programme regulations) |
| Requisites:
| This unit is not normally available to visiting/exchange students. |
| Description:
| Aims: To consolidate and extend topics met at A-level. To improve students' fluency and understanding of the basic techniques required for engineering analysis. Learning Outcomes: After taking this unit the student should be able to: * Solve certain classes of ODE. * Perform Laplace Transforms and their inverse. * Determine probabilities of events and sequences of events. * Determine probabilities and find means and standard deviations of both discrete and continuous probability distributions. * Statistical testing. * Find eigenvalues and eigenvectors of square matrices. * Perform least-squares fitting of data. Skills: Numeracy; working independently. Content: Ordinary differential equations: classification; reduction to first order form; 1st order nonlinear equations, variables-separable equations, linear constant coefficient equations. Laplace Transforms: definition; examples; transforms of derivatives; unit pulse, impulse and step function; shift theorems in s and t; solution of linear constant-coefficient ODEs, convolution theorem. Probability: trial, outcome, sample space and event; use of Venn diagrams; simple probability; complementation and addition rules; conditional probability; independent events; sampling; probability relating to sequences of events. Probability distributions: discrete and continuous distributions; mean, median, mode, percentiles and standard deviation; Poisson distribution; normal distribution. Statistics: hypothesis testing. Matrices: Gaussian elimination; eigenvalues and eigenvectors. Miscellaneous topics: least squares fitting of data. |