I have now completed units 1, 2 and 3 of the Open University course MST209 (Mathematical Methods and Models). This is self study and after a quick recap on vector algebra tomorrow and Tuesday; I will have set myself up for a few weeks of Vector Calculus practice, before Christmas creeps any closer.
Unit 3 mainly developed some basic calculus involving second order differential equations. Time allowed me to manage about 75% of the example questions, selecting at least one example for each different 'issue' that arises when trying to solve these equations.
I found it particularly satisfying when the second order diff equations were used to model damping phenomena in oscillating systems. I will probably look to try and use some of these example questions to test drive some different types of modelling software, before settling on one package to then master over the next two years.
However, I am quite unsure as to which software I should invest the time and effort into learning.
I have some experience of the algebra package Mathcad, but I found it quite difficult to use and didn't really warm to it. I know they are planning an easier product in the future, and I will test drive that software as part of my selection process. Other choices might be Mathematica, Matlab, Maple etc.
I need to do some research here, as I am unsure as to whether there is one package that is mainly used as an academic and industry standard, when modelling mathematical and physical systems or designs.
I suspect there isn't just one' best-fit' package, so it may just come down to personal preference, ease of use and checking that it has the scope to be used in my research and beyond.
I would go for MATLAB or it's free equivalent SCILAB. Which is fine for most types of problem you would use at undergraduate or even MSc level
ReplyDeleteLarge scale programs tend to be written in one of the main Languages. I still use FORTRAN but these days the main code of use is C# so its probably best to get some experience in that as well. Of course for large scale problems of the type in industry or say Astrophysical modelling of intergalatic collisions then you need access to a large parallel computer which only research institutions will have access to.
Don't forget there is the OU group I set up for looking at the Cambridge Numerical projects which should give you plenty of ideas. I suggest to complement your study of differential equations that the one on numerical techniques for differential equations would be a good starting point
Best wishes Chris
I agree with Chris that Matlab is a good choice for numerical calculations (or Octave, which is another free implementation). However, it doesn't do symbolic computation (like evaluating integrals) without the add-on symbolic mathematics toolbox, which is based on Maple. If you think you might later want to take some of the courses in the OU MSc programme, then M833 and the applied option of M840 use Maple.
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