Credits:
 6 
Level:
 Intermediate (FHEQ level 5) 
Period: 
Semester 1

Assessment:
 EX 100% 
Supplementary Assessment:  MA20220 Mandatory extra work (where allowed by programme regulations) 
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 
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.
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: 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 (Fulltime)  Year 2
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 2
 USMAAFB01 : BSc (hons) Mathematics and Statistics (Fulltime)  Year 2
 USMAAKB02 : BSc (hons) Mathematics and Statistics (Fulltime with Thick Sandwich Placement)  Year 2
 USMAAAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 2
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 2
Department of Physics
 USXXAFB03 : BSc (hons) Mathematics and Physics (Fulltime)  Year 2
 USXXAKB04 : BSc (hons) Mathematics and Physics with Placement (Fulltime with Thick Sandwich Placement)  Year 2
 USXXAAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 2
 USXXAFM01 : MSci (hons) Mathematics and Physics (Fulltime)  Year 2
MA20220 is Optional on the following programmes:
Programmes in Natural Sciences
 UXXXAFB01 : BSc (hons) Natural Sciences (Fulltime)  Year 3
 UXXXAKB02 : BSc (hons) Natural Sciences with Industrial Placement (Fulltime with Thick Sandwich Placement)  Year 4
 UXXXAAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 2
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 2
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 2
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 2
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 3
 USMAAKB06 : BSc (hons) Statistics (Fulltime with Thick Sandwich Placement)  Year 2
 USMAAKB06 : BSc (hons) Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB06 : BSc (hons) Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 2
 USMAAAB06 : BSc (hons) Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 2
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 2
