2018/19 Undergraduate Module Catalogue

MATH2375 Linear Differential Equations and Transforms

15 creditsClass Size: 340

Module manager: Professor Alexander Mikhailov
Email: A.V.Mikhailov@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2018/19

Pre-requisite qualifications

(MATH1012 or MATH1400) and MATH2365, or equivalent.

This module is approved as a discovery module

Module summary

This module introduces a variety of techniques for the solution, subject to suitable boundary and initial conditions, of the basic Partial Differential Equations of mathematical physics, which describe such ubiquitous phenomena as waves and diffusion.

Objectives

On completion of this module, students should be able to:

a) obtain power series solutions of 2nd order homogeneous linear Ordinary Differential Equations;
b) put a 2nd order linear differential operator into Sturm-Liouville form and use recursive procedures to find families of orthogonal eigenfunctions;
c) solve the standard Partial Differential Equations of mathematical physics in Cartesian or (2D or 3D) polar coordinates subject to given boundary conditions by the method of separation of variables;
d) use Fourier series and Fourier transform techniques to solve a range of initial boundary value problems for linear Partial Differential Equations.

Syllabus

Power series solution of Ordinary Differential Equations. Inner products and Sturm-Liouville operators and orthogonality of eigenfunctions. Bessel and Legendre functions, their basic properties and application. Fourier series and transforms, with applications to initial boundary value problems. Separation of variables, applied to the standard Partial Differential Equations of mathematical physics.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	10	1.00	10.00
Lecture	33	1.00	33.00
Independent online learning hours			7.00
Private study hours			100.00
Total Contact hours			43.00
Total hours (100hr per 10 credits)			150.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular examples sheets.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 20/03/2018

Disclaimer

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