## 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 2020/21

### Pre-requisite qualifications

(MATH1005 or 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Workshop 10 1.00 10.00 Lecture 22 1.00 22.00 Independent online learning hours 7.00 Private study hours 111.00 Total Contact hours 32.00 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

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 Open Book exam 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