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MA20220: Ordinary differential equations and control

[Page last updated: 10 August 2020]

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Intermediate (FHEQ level 5)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA10207 AND take MA10209 AND take MA10210 AND take MA10230
Before or 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; introduction to distributions, including the delta distribution.
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; solution of integral equations.
Linear control systems: state-space; impulse response; transfer functions; realizations; input-output stability; high-gain feedback; integral control.
Further information on programme availabilityProgramme 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 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-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)
  • 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)

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