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    Math Applied Math PhD Industry Job Prospects

    That is certainly worrying. Your experience in particular makes me think that at the very least, it might be a good idea to leave for awhile but not to swear off grad school completely
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    Math Applied Math PhD Industry Job Prospects

    Hahaha somehow, I didn't answer those questions in binary, though I would have done before grad school. That's the thing - I feel like grad school has crushed a lot of my spirit, but I'm willing to go through it if it'll substantially help me
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    Math Applied Math PhD Industry Job Prospects

    Hmm, that's really interesting and a lot to think about. Do you think MS grads are at any substantial disadvantage in terms of salary and employment compared to PhD grads? I have no desire whatsoever to stay in academia, even to get a PhD unless it seems like it would help me down the road...
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    Math Applied Math PhD Industry Job Prospects

    Hmm, that's interesting. The professors I spoke to, I asked them more generally what applied math PhDs are doing in industry, not theirs in particular, but I imagine that their own students would be the first examples to come to mind. Maybe that's a good reason to get out of the program unless...
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    Math Applied Math PhD Industry Job Prospects

    I've talked to a few professors about this, but none of them know anything outside academia. That was part of what made me want to leave - that academic disconnect with the outside world
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    Anyone considering a career as a patent attorney?

    I'm a graduate student in applied math. I've received my MS and am debating on continuing on for my PhD. How much would having the PhD over the MS help me if I were to become a patent lawyer? Also, I'd heard that the patent legal market was the one area that was still doing well in terms of...
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    Continue with my AM PhD program or go into patent law?

    I'm still in limbo, sort of spinning my wheels. I have contact with a professor who seems interested in me, and I think I can get it to work... but I really just don't want to
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    Math Applied Math PhD Industry Job Prospects

    I don't really have anything to add. I'm in a similar position - I now have my MS in applied math and am trying to decide if I want to stay on for my PhD
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    Continue with my AM PhD program or go into patent law?

    I'm beginning my second year in my PhD program. I had to fight very hard to make it to the second year, as my program condenses the normal two year masters sequence that would make up the beginning of other programs into one year. They were also very eager to cut students using prelims, so the...
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    Mathematica plot question, dsolve

    Two things: In your DSolve[] command, change b to b[a]. Second, if it's not plotting properly, it's for two reasons. You're using a lin-log plot to plot the answer, and the answer has imaginary components. Also, you have a second order equation with only one boundary condition. I assume that...
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    What is the difference between an excitable system and a relaxation oscillator?

    Homework Statement Consider the following set of differential equations: \begin{eqnarray*} \dot{u} & = & b(v-u)(\alpha+u^2)-u \\ \dot{v} & = & c-u \end{eqnarray*} The parameters b \gg 1 and \alpha \ll 1 are fixed, with 8\alpha b < 1. Show that the system exhibits relaxation...
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    Greek student going for grad studies in USA

    Hello! First off, you're still a freshman. Don't worry about grad school just yet! College is for more than finding what you want to do immediately and getting tunnel vision. You may decide to go into a different field entirely, or possibly not want to do grad school at all (and from what I...
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    Induction on the n-dimensional, radially symmetric wave equation

    Homework Statement Consider the radially symmetric wave equation in n dimensions u_{tt} = u_{rr} + \frac{n-1}{r}u_r Use induction to show that the solution is u = \left(\frac{1}{r}\frac{\partial}{\partial r}\right)^{(n-3)/2} \frac{f(t-r)}{r} for n odd and u =...
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    Definite integral evaluation (Inverse Fourier Sine Transform)

    That worked beautifully, vela. Thank you!
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    Definite integral evaluation (Inverse Fourier Sine Transform)

    I think that last integral may be the right way to do it, since \int_0^{\infty}\ e^{-k}/\sqrt{k}\ dk \propto Erf(\sqrt{k})
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    Integration by parts formula

    You're quite right for what z is. As for integration by parts, they are using it - I recommend looking up tabular integration.
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    Definite integral evaluation (Inverse Fourier Sine Transform)

    Homework Statement I'm working on a long problem and have come to the final step. The answer seems so simple, but I can't quite get to it. I need to evaluate this integral: \int_0^{\infty}\ \left(e^{-k^2 t}/k\right)\sin(kx)\ dk Homework Equations Mathematica gives the result as...
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    Black-Scholes equation (a type of diffusion equation)

    I'm noticing that the solution doesn't even look separable
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    AP Physics C in 3 weeks?

    I think that if you've got a good enough grasp of calculus and differential equations, you ought to be able to handle the mechanics exam. They do give you a formula sheet
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    Modeling - Reciprocal Function

    Your version really only involves one constant, since A / (Bx) = (A/B) * (1/x) = C/x, where C = A/B. So you're essentially trying to fit two points to a one-parameter family, which isn't always guaranteed. I'd try writing y = A / (x + B). If you have three points, you can try y = A / (Bx +...
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    Programs Should I accept this PhD position? I already have my MS. What is it like? (A. Math)

    That is a good idea. I don't really have anything to go to if I left grad school. I'm just feeling so burnt out. It really sapped a lot of my love for the subject. I talked to a career counselor at my school today, who advised me to take it since there would be more job recruiters in the...
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    Black-Scholes equation (a type of diffusion equation)

    Homework Statement The equation for the probability distribution of the price of a call option is \frac{\partial P}{\partial t} = \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 P}{\partial S^2} + rS\frac{\partial P}{\partial S} - rP with the conditions P(0,t) = 0, P(S,0) = \max(S-K,0), and...
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    Programs Should I accept this PhD position? I already have my MS. What is it like? (A. Math)

    The honest, but stupid, answer is that it never occurred to me. Same with engineering. I declared as a math major early on in college due to pressure from a math professor, and declared physics as a second major shortly thereafter. The thought of switching to engineering/finance just never...
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    Programs Should I accept this PhD position? I already have my MS. What is it like? (A. Math)

    Backstory (feel free to skip): Last year, I applied to a bunch of PhD programs in applied math. I got accepted into a couple, but Northwestern offered me an interesting option. They rejected me from the PhD program, but they said that they would accept me into a masters program (which I'd have...
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    Laplace's equation with unusual boundary conditions

    Wow, thank you for all the thought you've put into this! I'm confused though about how you went from the real axis into y > 0
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    Rolles Theorem

    First off, 2 isn't entirely correct - there are functions which are continuous but not differentiable (e.g. absolute value). As for the third part, it might be easier to make a change of variables: y = 5x. Then you're looking at cos y. What's the interval this would be on? It'd be...
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    Laplace's equation with unusual boundary conditions

    It seems like you'd want to apply a transformation of some sort to the equation that also hits the boundary condition.
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    Laplace's equation with unusual boundary conditions

    That's a very clever idea! I like it. Like you said, though, the solution to that is weird - plus since you now have a second order ODE, wouldn't you need two boundary conditions? We have one: u(0,0) = 1. It seems like the only other boundary condition that would make sense is that the...
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    Trying to find the radius of convergence of this complicated infinite series

    Here's a thought. k is just some positive integer, right? The issue of convergence of a series arises in the "tail" of the series - that is, if you want to look at the convergence of \sum_{i=0}^{\infty}\ a_n x^n, you could just as easily look at the convergence of \sum_{i=N}^{\infty}\ a_n...
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    Derivative of a function at a isolated point

    I agree with that. However, in order for the derivative to exist, you still must have values for f(x-δ) and f(x+δ), which you would not have in a singleton domain.
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