MA20220: Ordinary differential equations and control
[Page last updated: 05 August 2021]
Academic Year:  2021/2 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Intermediate (FHEQ level 5) 
Period: 
 Semester 1

Assessment Summary:  EX 100% 
Assessment Detail:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

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 controlrelated 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; RouthHurwitz 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: statespace; impulse response; transfer functions; realizations; inputoutput stability; highgain feedback; integral control.

Programme availability: 
MA20220 is Compulsory on the following programmes:
Department of Mathematical Sciences
 USMAAFB13 : BSc(Hons) Mathematics (Year 2)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 2)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 2)
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 2)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 2)
MA20220 is Optional on the following programmes:
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 2)
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB05 : BSc(Hons) Statistics (Year 2)
 USMAAFB05 : BSc(Hons) Statistics (Year 3)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 2)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 2)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 2)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)

Notes:  This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
 Programmes and units are subject to change in accordance with normal University procedures.
 Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any prerequisite rules.
 Find out more about these and other important University terms and conditions here.
