Further Pure 3 vs Differential Equations (MEI)

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Sal.Tek_ 〔サルテック〕
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Hello, I need to choose an extra module and I don't really fancy doing any extra mechanics/stats (for now) so it's between FP3 and DE.

I'm currently really enjoying the numerical differential methods in NC such as Euler's and the Runge-Kutta methods, so learning some analytical differentiation methods sounds quite nice as well as applying differential equations to the real world. On the other hand the multi-variable calculus and differential geometry also looks very nice.

Are there any particular merits to each module? Which one of those 2 would you recommend? The coursework component of DE doesn't bother me as my college have already said they can mark it.

Thank you in advance
Sal
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HapaxOromenon3
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(Original post by Sal.Tek_ 〔サルテック〕)
Hello, I need to choose an extra module and I don't really fancy doing any extra mechanics/stats (for now) so it's between FP3 and DE.

I'm currently really enjoying the numerical differential methods in NC such as Euler's and the Runge-Kutta methods, so learning some analytical differentiation methods sounds quite nice as well as applying differential equations to the real world. On the other hand the multi-variable calculus and differential geometry also looks very nice.

Are there any particular merits to each module? Which one of those 2 would you recommend? The coursework component of DE doesn't bother me as my college have already said they can mark it.

Thank you in advance
Sal
FP3 is better preparation for university since stuff like multivariable calculus and group theory is typically core content in the first year of your degree, so if you know it already, you'll be at a great advantage.

DE is essentially just a bunch of methods for solving different types of differential equations, which you have to memorise and practise. In this way I would find it quite boring, but your experience may be completely different, especially as you said you have enjoyed the numerical solution of differential equations in NC. You should also bear in mind that thee coursework is marked quite rigidly in that if you do the list of things in the mark scheme, you will get full marks, but as a result, it's quite easy to lose maks for simple accidental errors and omissions.
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Sal.Tek_ 〔サルテック〕
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Thank you for that information, FP3 seems like the best way to go especially in the event I'm forced to take a gap year, the exam is slightly cheaper as well If I was to do FP3 it seems it would be best to do multi-variable calculus group theory and one other thing. How useful is differential geometry? It looks very fun, but would something else be a better step before uni?

Thanks again in advance
Sal
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HapaxOromenon3
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(Original post by Sal.Tek_ 〔サルテック〕)
Thank you for that information, FP3 seems like the best way to go especially in the event I'm forced to take a gap year, the exam is slightly cheaper as well If I was to do FP3 it seems it would be best to do multi-variable calculus group theory and one other thing. How useful is differential geometry? It looks very fun, but would something else be a better step before uni?

Thanks again in advance
Sal
Differential geometry is interesting and probably quite different to anything you've done before. At university you wouldn't study it until the third year, and this would be at a much higher level than the MEI module. Nevertheless, the content of the module is certainly a good introduction.

As for the other options: vectors builds on the work you did in C4, but there's a lot of formulae that have to be memorised (shortest distance from a point to a line, point to plane, line to plane, etc) as deriving them on the spot is quite involved and difficult. Markov chains is quite easy and has some applications to the real world, but requires a graphical calculator that can handle matrices. At university you might study it as part of a probability module - depends on the precise course that you'll be doing.

Hopefully some of this information is helpful to you.
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Sal.Tek_ 〔サルテック〕
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Very, thank you very much!
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