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  1. J

    Differentiability of a complex function.

    (PROBLEM SOLVED) I am trying to think of a complex function that is nowhere differentiable except at the origin and on the circle of radius 1, centered at the origin. I have tried using the Cauchy-Riemann equations (where f(x+iy)=u(x,y)+iv(x,y)) \frac{\partial u}{\partial x}=\frac{\partial...
  2. J

    Perturbation Theory Formulas

    Thank you very much for the suggestion. I am working with a non-degenerate case so I'll take a look.
  3. J

    Perturbation Theory Formulas

    Does anybody happen to know where to find the perturbation theory formulas for the energies and states up to fourth order? I have to do a calculation up to this order and don't want to have to derive them if I don't have to (I know that Wikipedia has high order energies, but they only have the...
  4. J

    Trouble with use of the Residue Theorem

    Ah!! Thank you very much for that insight, it hit me as soon as I read what you had to say. I haven't used that trick in awhile so I think I temporarily forgot about it.
  5. J

    Trouble with use of the Residue Theorem

    I have just learned the residue theorem and am attempting to apply it to this intergral. \int_{0}^{\infty}\frac{dx}{x^3+a^3}=\frac{2\pi}{3\sqrt{3}a^2} where a is real and greater than 0. I want to take a ray going out at \theta=0 and another at \theta=\frac{2\pi}{3} and connect them with an...
  6. J

    Newton's third law of motion - help me to explain it to someone

    Newton's third law of motion is specifically describing forces. If I am at rest and a particle hits me with a force, \mathbf{\vec{F}}, then it feels a force exerted by me equal to -\mathbf{\vec{F}}.
  7. J

    Easy stuff, i'm just retarded

    Well you know that by the properties of integrals, you can treat it as two integrals I=I_1+I_2=\left(\int 1dt\right)+\left(-\int\cos{t}dt\right) Do you know these integrals? What is the derivative of -\sin{t}?
  8. J

    Differntiable at point problem

    So you have the function f(x)=\frac{x}{3x+1} and you know that a function is differentiable at a if its derivative exists at a. You also know that \left.\frac{df}{dx}\right|_{a}\equiv \lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h}=\frac{\frac{a+h}{3(a+h)+1}-\frac{a}{3a+1}}{h} If you simplify...
  9. J

    Length of curve in Polar coordinate system

    You can think of it like an infinitesimal form of the Euclidean distance formula. For a function f(t)=\langle x_1(t),x_2(t),x_3(t),\ldots\rangle \sum_a^b \sqrt { \Delta x_1^2 + \Delta x_2^2+\Delta x_3^2+\ldots } \longrightarrow s=\int_{a}^{b} \sqrt { dx_1^2 + dx_2^2+dx_3^2+\ldots} =...
  10. J

    Retake General GRE?

    It is for physics, and I feel like I actually did very well on the writing portion so that should be alright. Thanks for your response; it's hard getting a feel for what carries what weight on applications and what meets the expected standards, especially with the general GRE.
  11. J

    Retake General GRE?

    I just took the General GRE and recieved V: 560 Q: 740. Would it be advisable to take it again, or would the improvement in quantitative not matter that much? Thanks for any advice.
  12. J

    Mathematica Question (Matrix Multiplication)

    Ahh, thank you very much.
  13. J

    Mathematica Question (Matrix Multiplication)

    I figured it out now using a Do[] command, but my point was that if you want to multiply many matrices and not write out the long stretch of A1.A2.A3.A4....AN, then you cannot use the product command on Mathematica because that will just multiply the matrices element-wise. I wanted to know if...
  14. J

    Mathematica Question (Matrix Multiplication)

    I am trying to compute the following, \prod_{j=0}^{N-1}\left[\hat{I}+\hat{M(j)}\left(\frac{T}{N}\right)\right] where \hat{I}, \hat{M(j)} are matrices. My problem is that Mathematica interprets this product as element-wise with respect to the matrices, but I of course want it to use matrix...
  15. J

    Laplace transforms and ODE

    I think you got caught up in some simple confusion. The Laplace Transform transforms a function of some variable (it could be x or t or whatever) to a function of s by the rule F(s)=\int_{0}^{\infty}f(t)e^{-st}dt So in your case f(x)\longrightarrow F(s) and your equation will go...
  16. J

    Find the equation of the line of intersection of the planes:

    There are two parts two a problem like this. First you'll want to find the direction of the line of intersection, which is nothing but the cross product of the normal vectors of the planes, i.e. \mathbf{n_1}\times\mathbf{n_2}=\langle 2,-1,-1\rangle \times \langle 1,2,3\rangle. Then all you need...
  17. J

    How good Feynman Lectures are ?

    Halliday/Resnick Fundamentals of Physics is an excellent introductory text.
  18. J

    Derivative Problem

    No problem. Watch out though, I think you have a sign error in there. f'(x)=-e-x+2e-2x=0 So then 2e-2x=e-x and therefore by dividing you get 2=e-x+2x
  19. J

    Derivative Problem

    Double check your derivative, you shouldn't be bringing an x down right? The derivative of ecx for a constant c is just cecx
  20. J

    Question on Galois Group

    Yes that makes sense that its a Galois extension, because we're told that each of the roots are distinct (and there are n of them) so it is a splitting field and has characteristic 0, thus it's Galois. Although your argument makes perfect sense, saying that |GalQQ(z)|=[Q(z):Q]=1 if the group is...
  21. J

    Question on Galois Group

    I am trying to show that if z, z2, z3, ..., zn=1 are n distinct roots of xn-1 in some extension field of Q (the rationals), then GalQQ(z) (the galois group of Q(z) over Q) is abelian. Would I be wrong to say that since the galois group we're talking about here only involves an extension field...
  22. J

    Finite Field Question

    Ahh you're right! I was being distracted; all I need is Fermat's Little Theorem. Thanks a lot.
  23. J

    Finite Field Question

    I am trying to prove that if c is a root of f(x) in Z_p then c^p is also a root. It seems very simple but I can't think how to approach it. Any insight on this would be greatly appreciated, and sorry for not using the latex but it seems to be acting up.
  24. J

    Halliday physics vs. feynman lectures

    I'd say ideally use them in conjunction; fenyman's lectures are wonderful in terms of conceptual understanding but i think halliday is good for the wide-scope of details and problem solving.
  25. J

    Alternating Groups

    No problem
  26. J

    Alternating Groups

    If you go by the fact that the order of any alternating group is n!/2 then you would have that the order of A_2 is 2!/2=1 and therefore it's just the trivial group consisting of the identity element. Anything in the form of (wx) would be an odd permutation and therefore not in A_2
  27. J

    Simple Field Extension Question

    Oh wow yea, ok it's pretty clear. I think I was complicating things. Thanks.
  28. J

    Simple Field Extension Question

    I'm currently trying to prove that (for a field extension K of the field F) if u\in K and u^2 is algebraic over F then u is algebraic over K. I thought of trying to prove it as contrapositive but that got me nowhere--it seems so simple but I don't know what to use for this. Any help with this...
  29. J

    What is the de Broglie wavelength of this electron?

    The deBroglie wavelength is given by the relation \lambda = \frac{h}{p} where h is the plank constant and p is momentum. I'm assuming the number in eV you were given is the kinetic energy of the electron--you can look up its mass to get it in terms of momentum through T \text{(kinetic...
  30. J

    Need help with differential eq. from book

    To solve differential equations in the form y'+P(x)y=Q(x) it is useful to use an integrating factor defined by \mu=\exp{\left(\int P(x)dx\right)} We multiply both sides of the equation by this, \mu y'+\mu P(x)y=\mu Q(x) and if you look closely the left hand side is the...
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