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Programme & Unit Catalogues

## MA20220: Ordinary differential equations and control

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:
• Examination (EX 100%)
Supplementary Assessment:
MA20220 Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this module you must take MA10207 AND take MA10209 AND take MA10210 AND ( take MA10208 OR take MA10236 )
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.
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 (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-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)
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)

 Notes: This unit catalogue is applicable for the 2016/17 academic year only. Students continuing their studies into 2017/18 and beyond should not assume that this unit will be available in future years in the format displayed here for 2016/17. 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 pre-requisite rules. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.