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What is the most difficult topic in PDE?

  1. Jun 5, 2012 #1
    I am taking it in a few weeks, could someone tell me which topic are generally more challenging? PDE is Partial Differential Equations.

    Thank you
     
  2. jcsd
  3. Jun 5, 2012 #2

    Astronuc

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    As with ODEs, one starts with relatively simple PDEs and moves up to more complex equations and systems of equations.

    In order of complexity, time dependent PDEs, and then systems of PDEs, and finally non-linear PDEs.

    Just relax and enjoy.
     
  4. Jun 5, 2012 #3
    Navier Stokes or MHD Equations are unsolvable as far as I know.
     
  5. Jun 5, 2012 #4
    MHD equations are solvable via linear perturbation. You throw away every term that's nonlinear! But overall, most PDEs are not solvable in nature without making approximations.

    Transport equations can generally be solved only using numerical methods.

    As for the actual course itself, I'd have to say that the Bessel functions always got me the best of me when I took my first course in PDE.
     
  6. Jun 6, 2012 #5
    Well there a lot of unsolved problems in PDEs. I would say those are quite card.
     
  7. Jun 6, 2012 #6
    If it's a standard first quarter/semester course for me the most difficult aspect was fourier analysis due to the different types of convergence. I had not taken real analysis so learning about uniform, pointwise and L convergences was more challenging the rest of the material.

    Otherwise, solving PDE's (in an intro course) is pretty easy. If it's fairly standard, you'll probably cover the wave equation on the full line, diffusion equation on the full line, separation of variables and laplaces equation + a few other topics your instructor will pick that probably differ from person to person.
     
  8. Jun 6, 2012 #7
    Some useful special cases of the Navier-Stokes equations are solvable analytically.
     
  9. Jun 6, 2012 #8
    To me, knowing which topic in a class is more challenging is actually hindering. You get worked up thinking about how you will tackle this topic differently than the others and stress yourself out. The best way to go about it is taking the topics as they come, read the relevant material, and work on practice problems until you can solve the problem without any pain or suffering (outside of wrist pain).
     
  10. Jun 7, 2012 #9
    Is the concept of "Convolution", "unit-step functions in Laplace", or "dirac delta" heavily used in PDE? It's an intro class by the way...
     
  11. Jun 7, 2012 #10
    It's not like those are separate chapters in books. Convolutions comes up, heavyside functions come up and sometimes you want to take their laplace transform, the dirac delta function comes up, etc, etc. They're used, yeah.

    That being said, that sounds more like 2nd semester stuff.
     
  12. Jun 8, 2012 #11
    They all come up. The standard euristic solution to the cauchy problem for heat equation IS a convolution of. The dirac delta comes up especially if you mention distributions, so pretty much everytime you hear about "fundamental solution(s)" etc.
     
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