 Academic Year:
| 2015/6 |
| Owning Department/School:
| Department of Mathematical Sciences |
| Credits:
| 6 |
| Level:
| Intermediate (FHEQ level 5) |
| Period: |
Semester 1
|
| Assessment Summary:
| EX 100% |
| Assessment Detail: | |
| Supplementary Assessment: |
MA20220 Mandatory extra work (where allowed by programme regulations)
|
| Requisites: |
Before taking this module you must take MA10207 AND take MA10208 AND take MA10209 AND take MA10210
While taking this module you must take MA20216
|
| 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.
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| Programme availability: |
MA20220 is Compulsory on the following programmes:
Department of Mathematical Sciences
- USMA-AFB13 : BSc(Hons) Mathematics (Year 2)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
Department of Physics
- USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 2)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 2)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 2)
- USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 2)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 2)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 2)
MA20220 is Optional on the following programmes:
Department of Computer Science
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
Programmes in Natural Sciences
- UXXX-AFB01 : BSc(Hons) Natural Sciences (Year 3)
- UXXX-AAB02 : BSc(Hons) Natural Sciences with Study year abroad (Year 4)
- UXXX-AKB02 : BSc(Hons) Natural Sciences with Year long work placement (Year 4)
Department of Mathematical Sciences
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 2)
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 2)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFB05 : BSc(Hons) Statistics (Year 2)
- USMA-AFB05 : BSc(Hons) Statistics (Year 3)
- USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 2)
- USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
- USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 2)
- USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
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