Recent content by Justin Lazear

  1. J

    Infinite Resistor Network

    Since the network is infinite, if you extend the network by one more copy of the pattern, the equivalent resistance shouldn't change. So represent the network's resistance with a single resistor with Req resistance. Now, can you add 3 resistors to the Req resistor to make it back into the...
  2. J

    Have you noticed this?

    Don't worry, dex, it was intentional. tr.v. ef·fect·ed, ef·fect·ing, ef·fects 1. To bring into existence. --J
  3. J

    Have you noticed this?

    Well, the next time you start examining the effects of your particle accelerator bunny exterminator on cute pink flying bunny rabbits and wish it could effect them more, don't come complaining to me when you drown in your own pool of rabbits. --J
  4. J

    Solving a Differential Equation with a Fourier Series

    Looks like you got it. And just in case you were interested, here's some plots of the fourier series truncated to 5, 15, 50, and 500 terms. Can't even tell it's not the function itself in the 500 one, can ya'? Good job. --J
  5. J

    Solving a Differential Equation with a Fourier Series

    Looks good. Now go have another look at those b coefficients. --J Just one final left... Yay me!
  6. J

    Solving a Differential Equation with a Fourier Series

    You got an extra negative. \cos{n\pi} = (-1)^n, which we can verify by noting that when n = 0, n\pi = 0, so \cos{n\pi} = 1. Additionally, when n = 1, we just have cosine of pi, which is -1. So we must have (-1)n instead of (-1)n-1. --J
  7. J

    Have you noticed this?

    In what instances? Sometimes "affect" is the correct word, and sometimes "effect" is the correct word. Naturally, most of the English speakers in the world have no idea that they are not the same word, so it can be pretty irritating if it's one of your pet peeves. --J
  8. J

    Solving a Differential Equation with a Fourier Series

    You need to revisit your bn with your newly refound knowledge of the behavior of sine and cosine. The sign of your an term is indeed incorrect. Why do I let myself get dragged into other people's problems? *sighs* Back to finals! Work, damn me! --J
  9. J

    Laplace Initial Value Problem

    Unfortunately, it's a 30 hour drive that must be completed in one weekend. Sometimes I wonder about the things I get myself into... But there's a bubble bath waiting for me at the end of it, so it'll all be worth it. And while I'm driving for two days straight, you get to wander around in...
  10. J

    Double checking needed on 2 Differential Equations

    It's possible that your college has a license for it and will give it to you. Why don't you contact your IT department and ask? --J
  11. J

    Double checking needed on 2 Differential Equations

    Mathematica agrees with both of your solutions. Well done. --J
  12. J

    Laplace Initial Value Problem

    *sighs* If only I didn't have to write an essay and do a few more finals, move out of my room, then drive for 30-some-odd hours, I could look into it more. But alas, I've been screwed by finals week. :frown: So don't bust your butt on my account, salty, because I won't be able to do...
  13. J

    Series Diff EQ problem: (3 - x^2) y'' - (3x) y' - y = 0

    Also, you shouldn't include the xn in your coefficients. Remember that these are the coefficients of the powers of x! They don't include the power of x themselves. You must multiply them by the appropriate power of x to get your solution. Otherwise, it looks like you're set. Good job. --J
  14. J

    Series Diff EQ problem: (3 - x^2) y'' - (3x) y' - y = 0

    Your algebra is a little suspect. Try calculating those coefficients again. --J
  15. J

    Diff. EQ: How do I solve a 2nd order linear EQ with series?

    You know that there must be two arbitrary constants because the differential equation is of second order. You select the 0 and 1 constants because they are generally the most convenient when you have these problems that are designed to work out nicely. If your differential equation were instead...
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