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Multivariable Calc topics required for ODE?

  1. Oct 25, 2011 #1
    My school requires Calculus III before DEQ, though I had the department allow me to take the two concurrently. I am wondering what Calc III topics I should be fluent in to prepare for Differential Equations. I'm sure this university teaches DEQ with an understood previous knowledge in multivariable calc.

    My Calc II professor just said that it's basically the partial derivative, and it should take me a few minutes to learn how to do/use them.
     
  2. jcsd
  3. Oct 25, 2011 #2
    Yep. Partial derivative.
     
  4. Oct 25, 2011 #3
    That's it though??
     
  5. Oct 26, 2011 #4
    I took Calc III last spring and am taking an ODE class right now (same instructor even). Things that we have used from Calc III in ODE already (on quarters, so in week 4 of 10):

    Solving Exact Equations
    Solving Seperable Equations (was this a Calc II concept?)
    Slope Fields
    Partial Derivatives (and their manipulation)

    IMO - these are pretty intuitive concepts, and they shouldn't require more than a few hours and a few problems total to understand enough.

    Dependencies aside, some other things to consider:
    -What other classes are you taking? Calc III, ODE, and a Physics class seems like quite the rigorous load. 2hrs/night of homework for each easy. I've been spending as much time per night on my 3 credit ODE class as I did on my 4 credit Calc III class (which was after a 10 year break from Calc II! so I was even slower!).
    -Be careful about getting 'wires crossed' with concepts in the two classes. You might find a way to solve something in ODE that you're not meant to in Calc III (some of the slope-field interpretation comes to mind regarding this).
    -Some of the skills in Maple (or your choice of CA system) that I learned in Calc III have come in handy during some of the computer-oriented parts of ODE already (you can get away with using MS Excel for most things, minus the graphing part). This probably depends on your text and how in depth your instructors use computers.
     
  6. Oct 26, 2011 #5
    I don't think I will have problems with my workload for the semester. We covered seperable functions, well, so far, first order ones, in calc II. The other topics you mentioned are no problem. What specifically do you mean by "exact value" problems?
     
  7. Oct 26, 2011 #6
    I took the two classes at the same time. The only thing in common was an occasional partial derivative which took about 30s to figure out.

    Linear Algebra is the subject mostly used in ODE, I took LA after ODE (right now infact) its obvious that the two are very closely linked.

    Other than that you should be able to integrate single variable expressions
     
  8. Oct 26, 2011 #7
    Exact Equations are a particular form of a DE which was covered at the end of my Calc III in a bit of detail (form: M(x,y)dx + N(x,y)dy = 0 where My - Nx = 0). Using the condition above, an exact solution can be found. You've basically shown that M and N are related enough and you can 'merge' the equations after integrating.

    We've used them to solve certain type of problems in my ODE class, and they're mixed in with some other solutions to identify which technique should be used. I think they were presented as a good application of partial derivatives in Calc III (as they applied the concept that fxy = fyx).

    But, even with all this said - your school may have things broken up a little differently so this is all moot anyhow. Good luck.
     
  9. Oct 27, 2011 #8
    The only thing you might miss from multivariable calculus is the vector calculus bits, but these just really help with the intuition of solving differential equations, what they are, etc. but not really so much the calculations. Still, it's helpful to know this because it helps you to connect it to physics, but don't worry about that because you will probably get that intuition in a class like classical mechanics where differential equations are derived and you can see how they work. This is how it worked for me, I hardly learned anything in ODEs (partly on purpose, I found it irritating that I was just learning methods to solving funny looking equations) but in classical and quantum mechanics things became more clear.
     
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