Would learning PDEs also allow one to deal with ODEs?

[Ostonzi]

Are PDEs or ODEs more useful? Especially in biochemistry/molecular biology.

Would learning PDEs also allow one to deal with ODEs?

 

[dsking]

ODEs are essential to know before you start looking at PDEs. If you knew how to deal with PDEs and not ODEs that would be like knowing how to do multi-variable calculus before you knew single-variable. However, there are some exceptional ODE's, such as non-linear, that require different methods.

 

[Pengwuino]

One of the main techniques of PDEs is turning them into ODEs... so I would say ODEs are the most important.

 

[snipez90]

I think if you were doing evolutionary biology or computational biology, then knowing PDEs would be really crucial. For general biochem or molecular bio, I don't think they're that common of a tool?

You should have some requisite knowledge of ODEs before doing PDEs, but I would guess nothing more than the relevant pages on wikipedia. Also, you can PM me if you want resources for learning ODEs. Learning to solve basic ODEs requires nothing more than calculus, but knowing some real analysis is helpful and necessary if you want to understand issues such as existence of solutions.

 

[epenguin]

For 'biochemistry' grasp of linear ode's with constant coefficients will see you through. A good grasp of that - matrix formulation, eigenvalues, eigenvectors which it does not take all that long to master will be an advantage. (Linearisation of nonlinear equations for local analysis which gives good idea of overall behaviours of unsolvable equations is then a fairly obvious application you might meet in the biomath reaches.) Being not thrown by matrices and a bit handy with them is good to have because in the systems you deal with not just one thing is happening at a time. Applications in kinetics and related rather physical biochemistry. That and any bit more does no harm for physical methods used in biochemistry.

But if you've got that much you'll be considered "the mathematician" among biochemists. Your classmates will be guys who are thrown by "v = s/(K + s) , then s = what? in terms of v and K". A few years ago at school they could do it when it was Exercise 3 of Chapter 5 math. But no one gave them the idea it would ever be used for anything or could mean anything outside Chapter 5. They might just still manage by dint of memory y = x/(K + x) but not v = s/(K + s)!

I'll always remember the words of one old biochem Prof. "Ah all right for you, you're a mathematician." I said Me!? I am not a mathematician by any stretch. "OK" he said "But you're not frightened of it, that's the big point"

Non-linear d.e.'s and pde's is pretty much outside 'biochemistry' and mol. biol. and a specialist area for evolutionary theory, 'biomath' modelling etc. There is plenty of help available for biochemists who do want to get into such areas. These areas are almost not a 'subject', more of a hotch-potch. I agree with snipez. lde's can't be escaped and shouldn't try - needed for even the background physics minimum.

More generally every kind of biologist now has to be quite interdisciplinary so learning of math is not really wasted. Beyond a certain point though a biochemist has to learn biochemistry!

 

[Simfish]

omg I never knew you would come here o_0

Anyways, look in a book like Murray's "introduction to mathematical biology" and look at the math used there.

 

[Ostonzi]

i heard PF has good academic advice. CC is useless.

what about for biomedical engineering? would i require more math like dynamics and chaos/fourier analysis/PDEs?

 

[Simfish]

Okay, here's a really good list of courses that would be useful: http://www.washington.edu/students/crscat/appmath.html (it's the #2 applied math department in the nation so it's certainly doing something right).

 

[Ostonzi]

Would this be enough Fourier analysis?
http://www.math.umn.edu/~olver/pdn.html

 

[Simfish]

Yes, definitely. Most of the Fourier analysis you need for science isn't enough to fit in one course.

There's also a way to do Fourier analysis with MATLAB (which is the type most useful for science, really), but you can do that without even knowing any of the theory.