Department of Mechanical Engineering, Unit Catalogue 2010/11 |
ME10304: Mathematics 1 |
 Credits:
| 6 |
| Level:
| Certificate |
| Period: | This unit is available in... |
| Semester 1 |
| Assessment:
| EX 100% |
| Supplementary Assessment: | ME10304 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: Handle circular and hyperbolic functions, and sketch curves. Differentiate and integrate elementary functions, products of functions etc. Use complex numbers. Employ standard vector and matrix techniques for geometrical purposes. Determine the Fourier series of a periodic function. Understand power series representations of functions and their convergence properties. Skills: Numeracy; working independently. Content: Elementary topics: curve sketching; hyperbolic and circular functions; identities; partial fractions; arithmetic and geometric progressions; binomial expansions. Differentiation: limit definition; notation; higher derivatives; standard derivatives; derivative of products and functions of functions; Taylor's series; partial differentiation; critical points. Integration: definition as an area; integration by substitution, using partial fractions; integration by parts; mean and RMS; surfaces and volumes of revolution. Complex numbers: definition; geometric representation; modulus and argument; Cartesian and polar forms; Euler's formula; elementary operations; roots. Vectors and Matrices: definition; unit vectors; classification of matrices; scalar and vector products and their use; geometrical applications; solutions of Ax=b systems; determinants. Fourier Series: definition; interpretation; use of symmetries; convergence properties. |