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 
Rabies in foxes 
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 

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 


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 
Spectral Methods for Nonlinear Wave Equations Singular Value Decomposition for Ocean Temperature Data 


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 Magnetic induction equation in 2D, flux expulsion 


Project 3 (cont): problem formulation, SVD; Project 4: problem formulation Project 1: comments on ode45; Project 4: (cont) background Project 4 (cont): formulation; numerical scheme, finitevolume method 
Week 6 
Project 4 Project 3 


Project 4 (cont): spatial discretisation; conservative scheme Project 4 (cont): time=stepping; DuFortFrankel leapfrog scheme Project 3 (cont): SVD derivation 
Week 7 
Project 3
Project 2 


Project 3 (cont): SVD derivation SVD for a linear operator, core surface operator Project 2 (cont): discrete Fourier series and transform 
Week 8 
Project 3
Project 2 


Project 3 (cont): svd(A) vs A*A’ and A‘*A zero singular and eigen values; Project 2 (cont): numerical scheme, fit, iffy and shifts Project 2 (cont): discrete Fourier series and transform 
Weeks 913 
There are problems with permissions on lecture recordings from Lecture 16 on Canvas. I am trying to fix this. Two algorithms on Projects 2, 3 or 4 (not the reported second project) is now due noon Wednesday 13 May: Note correction to Lecture 11 on Project 2. Second report on Projects 2, 3 or 4 is now due noon Wednesday 13 May. 

Week 9 
Symplectic Integrators



Project 6: Geometric integration, Hamiltonian systems, symplectic maps symplectic maps (cont), simple harmonic oscillator simple harmonic oscillator (cont), Euler's method, symplectic numerical integrators 
Week 10 
Numerical Integration of Stochastic Differential Equations Neural Networks 


Project 6 (cont): symplectic maps, symplectic integrators symplectic integrators (cont) Project 2 (cont) comments; Project 7: background, Wiener processes and numerical simulation 
Weeks 1113 
Second report on Projects 2, 3 or 4 is now due and algorithms on Projects 2, 3 or 4 is due noon Wednesday 13 May via turnitin. There is no need to email the files to me.
Note comment on Project 2 Q3: The method solves a periodic extension u of a truncation of the true solution The periodicity means (i) that boundary fluxes of conserved quantities exactly cancel, which is inherent to the numerical method not the conserved quantity; and (ii) that conserved quantities give information about the Fourier coefficients of u. How much information does the "mass" give about the Fourier coefficients of u? 

Week 11 
Project 7: Numerical Integration of Stochastic Differential Equations Project 8: Neural Networks Boussinesq Thermal Convection 


Project 7 (cont): Ito's formula; EulerMaruyama, Milstein stochastic numerical schemes Milstein scheme (cont); strong and weak convergence; Project 8: neural networks, foundations, modelling Project 8 (cont) Hebb's rule, Hopfield model; feedforward networks, 2layer networks 
Week 12 
Project 8: Neural Networks Project 5: Boussinesq Thermal Convection 


Project 8 (cont): gradient descent algorithm; Project 5: background Project 5 (cont): equations for mass, forces and momentum, temperature Project 5 (cont): Boussinesq approximation; solving equations 
Weeks 13  end 
Third report on Projects 5, 6, 7 or 8 is now due noon Wednesday 10 June via turnitin. Algorithms for the other projects are NOT required. The third report is now worth 33 marks. 

Week 13 
Project 5: Boussinesq Thermal Convection Project 9: Optimisation in a Trade Model 


Project 5 (cont): spectral expansions/equations/nonlinear terms in x Project 5 (cont): linear stabiity problem; solution of Poisson's equation, Matlab code. Project 9: Ricardo's model, absolute & comparative advantage Project 9 (cont): Gomory's Ricardo model with economies of scale, CobbDouglas utility, integer equilibria, upper bound on integer equilibria utilities 