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 timestepping; AdamsBashforth, AdamsMoulton 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

AdamsBashforth, AdamsMoulton and Gear methods (cont); Finitedifferences
Finitedifferences (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; RungeKutta methods
Secondorder CTCS (leapfrogging scheme); FTCS heat equation stability
CTCS heat equation stability; Q2 steadystate 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 513 
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, finitevolume 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; DuFortFrankel leapfrog scheme
Project (cont): SVD derivation
