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  1. M

    Showing the Difference Between an Ito Integral & Riemann Integrals.

    Hi Everyone, A problem I have here. I am trying to solve a problem involving Ito Integrals and Riemann interals. Homework Statement Prove \int^{T}_{0} tdW(t) = TW(T) -\int^{T}_{0} W(t)dt Homework Equations I want to solve this question WITHOUT using Ito's Lemma directly. The Attempt at...
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    Flow Velocity

    Hi Guys. I have an absurd problem and no idea to solve it. Please could you help me? \frac{u}{\hat u} = \left [ \frac{y}{R} \right ]^{1/n} = \left [1- \frac{r}{R} \right ]^{1/n} Suppose the turbulent flow velocity distribution in a pipe of Radius R can be described by the equation...
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    Laurent's Theorem

    hmm so for part (1) u_x = v_y = -u_x AND u_y = -v_x = v_x so u and v are constant because u_x = -u_x and -v_x = v_x is that correct?
  4. M

    Laurent's Theorem

    Hi just a bit of help needed here as I don;t know where to start: Part (A) ---------------------------- Suppose f(z) = u(x,y) + iv(x,y)\;and\;g(z) = v(x,y) + iu(x,y) are analytic in some domain D. Show that both u and v are constant functions..? I guess we have to use the CRE here but...
  5. M

    Differentiating Sin and Cos

    Hi. I believe this may have been addressed previously but I wanted to make sure since I don't think it was completed. Hi I know that differentiating sin = cos , and differentiating cos = -sin. Time to prove it. Q3: Prove that: \frac{d}{{dz}}\sin z = \cos z We know the McLaurin form...
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    D'Alembert's Wave. Seems Easy Or Maybe I'm Missing Something?

    D'Alembert's Wave. Seems Easy Or Maybe I'm Missing Something? Hi I have this D'Alembert's question. What I've done seems easy so I wanted to clarify just in case I'm missing something, cus it seems so easy. Second part I don't understand and would appreciate a guidance. (PART A) D'Alembert's...
  7. M

    Heat Equation Problem

    Hi. Thanks. I understand that I have to get the general solution in a Summation form so that I can apply the Fourier series. But I have a little difficulty on applying that new function you told me to introduce. This is how I've been taught to work out the solution: I'll try to explain...
  8. M

    Double Integrals

    upload the picture in mate it gives a direct link to the picture. good site for hosting pics.
  9. M

    Heat Equation Problem

    Hi. Having problems with this tricky Heat Equation Question. Managed to do part (a) and would appreciate verification that it's right. But I can't manage to finish off the second part. I've started it off so please do advice me. Thanks a lot! QUESTION...
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    Radius of convergence

    oh hi, yes i had to open a new account "rinatoc" because my mathfied account for some reason was giving an error whenever i tried logging in. i thought maybe my account got disabled or something so i opened the other one.. turned out to be some ip problem.. but then my mathfied account is...
  11. M

    Radius of convergence

    ok after a bit more studying, would this be correct: (A) Using Ratio Test: [\mathop {\lim }\limits_{k \to \infty } \left| {\frac{{a_{k + 1} }} {{a_k }}} \right| = \mathop {\lim }\limits_{k \to \infty } \left| {\frac{{(k + 1)^{113} 2^{ - (k + 1)} (z - 1)^{k + 1} }}{{k^{113} 2^{ - k} (z - 1)^k...
  12. M

    Laurent Series

    i get the idea of the laurent expansion but i get confused with the constraints and how they change the way you work with the expansion. by now you can prob. tell I am trying to get to grasp with complex analysis as a whole. for example i have this : find laurent series for :\[ f(z) =...
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    Cauchy Riemann & Taylor Expansion.

    QUESTION 4 Here's my attempt for QUESTION 4: \begin{gathered} \sin \theta = \frac{{e^{i\theta } - e^{ - i\theta } }} {{2i}} \hfill \\ \cos \theta = \frac{{e^{i\theta } + e^{ - i\theta } }} {2} \hfill \\ \hfill \\ \sin ^2 \theta = \left[ {\frac{{e^{i\theta } - e^{ -...
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    Cauchy Riemann & Taylor Expansion.

    Hi There. Was working on these and I think I managed to get most of them but still have a few niggling parts. I've managed to do questions 2,3,3Part2 and I've shown my working out so I'd be greatful if you could verify whether they are correct. Please could you also guide me on Q1 & 4. Q1...
  15. M

    Residue Problem.

    hi all, my first post; had a minor headache with this problem lol. PROBLEM 1: Finding Residue: ----------------- find Res(g,0) for g(z) = z^{-2}coshz My Attempt/Solution: ----------------- I know coshz = 1 + \frac{x^2}{2!} + \frac{z^4}{4!} ... so now z^{-2}coshz = z^{-2} (1 +...