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Programme & Unit Catalogues

## MA20220: Ordinary differential equations and control

Owning Department/School: Department of Mathematical Sciences
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 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.
Programme availability:

#### MA20220 is Compulsory on the following programmes:

Department of Mathematical Sciences
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 2
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 2
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
Department of Physics
• USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 2
• USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 2
• USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 2

#### MA20220 is Optional on the following programmes:

Department of Computer Science
• USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 3
• USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
• USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 3
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 2
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 2
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 2
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, 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 pre-requisite rules.