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Undergraduate Study

MATH4411 Applied Computational Mathematics

This page contains information on the Honours Mathematics unit Applied Computational Mathematics.

Lecturer for this course: David Ivers.

For general information on honours in the School of Mathematics and Statistics, refer to the relevant honours handbook.

For enrolled students or other authorized people only, here is a link to the Canvas page for MATH4411.

Resources

The information sheet outlines the course, projects for assessment and guidelines for writing up project reports, and their due dates.

Project Lecture notes Matlab codes Material covered
Week 1

Project 1

Rabies in foxes

Lecture 1

Lecture 2

Lecture 3, IVP's

Course outline, projects and project reports; Project 1 problem formulation

Project 1 problem formulation (cont)

IVP's and time-stepping; Adams-Bashforth, Adams-Moulton and Gear methods

Week 2

Project 1: Rabies in foxes

Lecture 4

Lecture 5, FD's

Lecture 6

 

ftcs_dji.m, ftcs_dat, annimate.m

rabies.dat

Adams-Bashforth, Adams-Moulton and Gear methods (cont); Finite-differences

Finite-differences (cont); FTCS scheme for heat equation

Method of lines, numerical scheme for Q1

Week 3

Project 1

Rabies in foxes

Lecture 7

Lecture 8, Interpolation

 

 

Lecture 9

 

 

 

 

ode45_dji.m, rhs45_dji.m

AB2 Matlab implementation; Runge-Kutta methods

Second-order CTCS (leap-frogging scheme); FTCS heat equation stability

CTCS heat equation stability; Q2 steady-state solution stability; Q5 ode45; Interpolation

Week 4

 

Project 2

Spectral Methods for Nonlinear Wave Equations

Project 3

Singular Value Decomposition for Ocean Temperature Data

Lecture 10

 

 

Lecture 11

 

Lecture 12

 

 

 

 

 

svd_image.m, temperature.dat

Interpolation (cont); AB2 local truncation error derivation

Project 2 problem formulation; numerical scheme

Project 3 problem formulation

Weeks 5-13

Lectures will be given online using zoom on the Math4411 Canvas webpage at the scheduled lecture times.

Lecture recordings from Lecture 16 and later will be available on Canvas.

Lecture notes will still be available on this webpage..

Online labs are Fri 1pm on zoom. Email me if you have any difficulties with programming, etc, etc. You should have access to the University Matlab licence on your laptop.

Project 1 is now due noon Wednesday 8 April.

Week 5

Project 3: Singular Value Decomposition for Ocean Temperature Data

Project 4

Magnetic induction equation in 2D, flux expulsion

Lecture 13

 

 

Lecture 14

 

Lecture 15

 

 

TBA

Project 1: comments on ode45; Project 4: (cont) background

Project 4 (cont): formulation; numerical scheme, finite-volume method

Week 6

Project 4

Project 3

Lecture 16

 

 

Lecture 17

 

Lecture 18

 

 

Project 4 (cont): spatial discretisation; conservative scheme

Project 4 (cont): time=stepping; DuFort-Frankel leapfrog scheme

Project (cont): SVD derivation