2008/09 Undergraduate Module Catalogue

MATH2375 Linear Differential Equations & Transforms

15 creditsClass Size: 250

Module manager: Dr M. Ivanchenko
Email: M.Ivanchenko@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

Pre-requisite qualifications

MATH2365 or equivalent

Pre-requisites

 MATH2365 Vector Calculus

This module is mutually exclusive with

 MATH2431 Fourier Series, Partial Differential Equations and Transform

Module replaces

MATH2370

This module is approved as an Elective

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, as well as the potential problems of gravitation, electromagnetism and fluid dynamics.

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) test 2nd order linear differential operators for symmetry and draw appropriate conclusions from the resulting orthogonality of their 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, using Bessel and Legendre functions where necessary;
d) use Fourier and Laplace transforms to solve a range of boundary and initial value problems for linear Ordinary Differential Equations and Partial Differential Equations.

Syllabus

Separation of variables, power series solution of Ordinary Differential Equations, symmetric operators and orthogonality of eigenfunctions, Bessel and Legendre functions, their basic properties and application to boundary and initial value problems. Fourier and Laplace transforms, with applications to boundary and initial value problems.

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 Example Class 17 1.00 17.00 Lecture 27 1.00 27.00 Independent online learning hours 7.00 Private study hours 99.00 Total Contact hours 44.00 Total hours (100hr per 10 credits) 150.00

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 Written Work Coursework 15.00 Total percentage (Assessment Coursework) 15.00

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

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 3 hr 85.00 Total percentage (Assessment Exams) 85.00

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