Some Lectures

Mathematical Methods

3rd year Geophysics : Lecture slides 1-3

Geology

4th year Geology : Foreland Basins

Mathematical methods

I like books with good examples. My favourite practical book on Mathematical Methods including Earth science examples is "A guided tour of mathematical methods in the physical sciences" by Roel Snieder. "Introduction to propbability models" by Ross gives a good introduction to probability theory. "The R book" gives an excellent description about statistical analysis, with practical examples of how to apply it in the free software R; Matlab will have similar functions.

Dimensional analysis

Buckingham Pi Theorem : Tells you how many non-dimensional parameters are described by a collection of variables. If you have N variables containing P dimensions then there are N-P dimensionless numbers that descibe the problem.

Original Buckingham Pi paper
Geomorphological example

Introduction to probability theory

When computers are bad at maths (By ciaran.beggan@ed.ac.uk)

"The accuracy of calculations on a modern computer is generally never questioned by users outside the realm of chip designers and mathematicians who are specialists. However, it might surprise you to know that the IEEE standard for the representation of floating point numbers on a computer is actually rather granular (i.e. the computer cannot represent a continuum of numbers). By dint of being a binary system, some numbers cannot be accurately represented e.g. the number 0.1 is actually more like 0.100000100000100.... While this is not generally an issue, for most researchers, I would like to give you an awareness of how errors, both absolute and relative, can creep into computational models, if the user believes that the computer cannot make a mistake. I will demonstrate how the IEEE standard works, show a couple of examples of how errors build up, the consequences of such errors and strategies to remove them by appropriate scaling of the problem and by taking care on the order of computation."

Examples
Matlab file

Requests and ideas

Regression
Numerical and computational errors
Greens functions
Time series analysis and correlations