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Undergraduate Study

AMH1   Computational Projects in Applied Mathematics

General Information

This page relates to the Applied Mathematics Honours course "Computational Projects in Applied 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.

Resources

The information sheet (Mar 24 update) outlines the course projects for assessment and their due dates.

Guidelines for writing up the report are outlined in the report style sheet.

Project Lecture notes Matlab codes Material covered
Week 1

Project 1

Rabies in foxes

Lecture 1

Lecture 2, IVP

Problem formulation

IVP's and time-stepping

Week 2

Project 1

Rabies in foxes

Lecture 3, FD's

Lecture 4

ftcs_dji.m, ftcs_dat, annimate.m

rhs45_dji.m

Multi-step, finite-differences, FTCS scheme

Method of lines, Project 1

Week 3

Project 2

Spectral methods for nonlinear wave equations

Lecture 5, DFT

Lecture 6

Project 1 (end)

Discrete Fourier transform

Fast Fourier transform, Project 2, spectral methods for de's

Week 4

Project 3

Applications of the singular value decomposition

Lecture 7

Lecture 8

svd_image.m

svd_image.m (windows,mac)

Fourier transform (more)

Project 2 (end)

Project 3, singular value decomposition

Week 5

Project 4

The expulsion of magnetic flux by convective eddies

(advection of a passive scalar)

Lecture 9

Lecture 10

Singular value decomposition (more), Project 3 (end)

Project 4, magnetic induction equation in 2D, flux expulsion

Week 6

Project 4

Expulsion of magnetic flux

Lecture 11

No lecture

Flux-conservative leapfrog scheme, weak diffusion

Project 4 (end)

Week 7

Project 5

Symplectic integration

No lecture

Lecture 12

Symplectic integration

Week 8

No lectures

Week 9

Project 5

Project 6

Stochastic DE's

Lecture 13

Lecture 14

Numerical symplectic integration, Project 5 (end)

Stochastic DE's, Wiener processes

Numerical integration schemes

Week 10

Project 6

Project 7

Neural Networks

Lecture 15

Lecture 16

Numerical integration schemes, Project 6 (end)

Neurons, layers, learning, feedforward networks

Numerical learning schemes, Project 7 (end)

Timetable

 

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