Credits:
 6 
Level:
 Honours (FHEQ level 6) 
Period: 
Semester 1

Assessment:
 EX 100% 
Supplementary Assessment:  MA30044 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:
 Before taking this unit you must take MA20216 and take MA20219 and take MA20220 and take MA20223 
Description:
 Aims & Learning Objectives: Aims: To furnish the student with a range of analytic techniques for the solution of ODEs and PDEs.
Objectives:
Students should be able to obtain the solution of certain ODEs and PDEs. They should also be aware of certain analytic properties associated with the solution e.g. uniqueness.
Content: SturmLiouville theory: Reality of eigenvalues. Orthogonality of eigenfunctions. Expansion in eigenfunctions. Approximation in mean square. Statement of completeness.
Fourier Transform: As a limit of Fourier series. Properties and applications to solution of differential equations. Frequency response of linear systems. Characteristic functions.
Linear and quasilinear firstorder PDEs in two and three independent variables: Characteristics. Integral surfaces. Uniqueness (without proof).
Linear and quasilinear secondorder PDEs in two independent variables: CauchyKovalevskaya theorem (without proof). Characteristic data. Lack of continuous dependence on initial data for Cauchy problem. Classification as elliptic, parabolic, and hyperbolic. Different standard forms. Constant and nonconstant coefficients.
Onedimensional wave equation: d'Alembert's solution. Uniqueness theorem for corresponding Cauchy problem (with data on a spacelike curve).

Programme availability:

MA30044 is Optional on the following programmes:
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 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 4
 USMAAFB13 : BSc (hons) Mathematics (Fulltime)  Year 3
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAFB01 : BSc (hons) Mathematics and Statistics (Fulltime)  Year 3
 USMAAKB02 : BSc (hons) Mathematics and Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 3
 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 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 3
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 4
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 TSMAAFM09 : MSc Mathematical Sciences (Fulltime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 2
 TSMAAFM08 : MSc Modern Applications of Mathematics (Fulltime)  Year 1
 TSMAAFL02 : PG Dip Modern Applications of Mathematics (Fulltime)  Year 1
Department of Physics
 USXXAFB03 : BSc (hons) Mathematics and Physics (Fulltime)  Year 3
 USXXAKB04 : BSc (hons) Mathematics and Physics with Placement (Fulltime with Thick Sandwich Placement)  Year 4
 USXXAAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
