Department of Mathematical Sciences, Unit Catalogue 2010/11 |
MA20220: Ordinary differential equations and control |
 Credits:
| 6 |
| Level:
| Intermediate |
| Period: | This unit is available in... |
| Semester 1 |
| Assessment:
| EX100 |
| Supplementary Assessment: | Supplementary assessment information not currently available (this will be added shortly) |
| Requisites:
| Before taking this unit you must take MA10207 and take MA10208 and take MA10209 and take MA10210 and while taking this unit you must take MA20216 or equivalent units from MA10001 - MA10006. You may not take this unit if you have already taken MA20009. |
| Description:
| Aims: This course will provide standard results and techniques for solving systems of linear autonomous differential equations, including Laplace transform methods. Based on this material an introduction to the ideas of mathematical control theory will be given, with emphasis on stability and feedback. Learning Outcomes: After taking this unit, students should be able to: * Show that they are conversant with the basic ideas in the theory of linear autonomous differential equations. * Employ Laplace transform and matrix methods for the solution of such equations. * Demonstrate familiarity with elementary concepts from linear control theory. * Solve basic control-related problems. * Write the relevant mathematical arguments in a precise and lucid fashion. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials). Content: Systems of linear ODEs: solution of homogeneous systems; linearly independent solutions; eigenvectors and generalized eigenvectors; fundamental matrices and matrix exponentials; exponential stability; Routh-Hurwitz criterion; solution of inhomogeneous systems by variation of parameters. Laplace transforms: statement of conditions for existence; properties including transforms of the first and higher derivatives, damping, delay; inversion by partial fractions; solution of ODEs; convolution theorem; delta functions; solution of integral equations. Linear control systems: state-space; impulse response; transfer functions; realizations; input-output stability; high-gain feedback; integral control. |