Recent content by compliant

  1. C

    Matrices with complex entries

    Homework Statement Let B be an m×n matrix with complex entries. Then by B* we denote the n×m matrix that is obtained by forming the transpose of B followed by taking the complex conjugate of each entry. For an n × n matrix A with complex entries, prove that if u*Au = 0 for all n × 1 column...
  2. C

    Fourier sine transform for Wave Equation

    But that only makes use of the regular Fourier Transform, and not the Fourier Cosine Transform.
  3. C

    Fourier sine transform for Wave Equation

    [PLAIN]http://img815.imageshack.us/img815/9894/fourier5313.png [Broken] there was a minus sign. oops. In any case, relevant equations: F_{c}(f(x,t)) = \sqrt{\frac{2}{\pi}} \int^{\infty}_{0} cos (\lambda x) f(x,t) dx F_{c}(f''(x,t)) = -\sqrt{\frac{2}{\pi}} f'(0,t) - \lambda^{2} F_{c}(f(x,t))...
  4. C

    Fourier sine transform for Wave Equation

    Homework Statement Find the solution u, via the Fourier sine/cosine transform, given: u_{tt}-c^{2}u_{xx}=0 IC: u(x,0) = u_{t}(x,0)=0 BC: u(x,t) bounded as x\rightarrow \infty , u_{x}(0,t) = g(t) 2. The attempt at a solution Taking the Fourier transform of the PDE, IC and BC...
  5. C

    Two springs connected by a spring

    Well, then I would have m_{2}\ddot{x_{2}}-m_{1}\ddot{x_{1}} = -kq ...which, from what I see, doesn't do a whole lot because I still can't factor the left side to do anything.
  6. C

    Two springs connected by a spring

    Homework Statement Two masses, m1 and m2, are connected to each other by a spring with a spring constant k. The system moves freely on a horizontal frictionless plane. Find the natural frequency of oscillation. Homework Equations F = -kx F = ma The Attempt at a Solution Let m1 be the mass...
  7. C

    Finite approximation of PDEs

    Homework Statement Given u_tt = F(x,t,u,u_x, u_xx), give the finite difference approximation of the pde (ie using u_x = (u(x + dx; t) - u(x - dx; t))/(2dx) etc.) Homework Equations Well, clearly, u_x = (u(x + dx; t) - u(x - dx; t))/(2dx) The Attempt at a Solution I really have no idea how...
  8. C

    Introductory PDE (diffusion equation)

    Homework Statement u_t = -{{u_{x}}_{x}} u(x,0) = e^{-x^2} Homework Equations The Attempt at a Solution The initial state is a bell curve centred at x=0. The second partial derivative of u at t=0 is {4x^2}{e^{-x^2}}, which is a Gaussian function, which means nothing to me other than its...
  9. C

    Double integrals in polar coordinates

    sorry to do this, but bump.
  10. C

    Double integrals in polar coordinates

    tiny-tim, thanks for those. desperately needed. hallsofivy, I did draw the diagram, and found that it was rather inconveniently symmetrical, which was why I got stumped. going by your suggestion, from θ = 0 to θ = π/2, I would be integrating along the right side of the curve, where the...
  11. C

    Double integrals in polar coordinates

    Homework Statement Find \int{\int_{D}x dA} where D is the region in Q1 between the circles x2+y2=4 and x2+y2=2x using only polar coordinates. The Attempt at a Solution Well, the two circles give me r=2 and r=2 cos \theta, and the integrand is going to be r2cos \theta, but I have no...
  12. C

    Max/min with partial derivatives

    *backtracks* ooooooooooookay. so. when x=0, f_x = -2, but f_x = 0, so x=0 is not a solution. which brings me back to the points (-1,0) and (1,2). looking at my calculations for (-1,0), turns out that it's horrendously wrong. At (-1,0), f_xx = -2(6-2) = -8, D = (-8)(-2) - (0-3+2)^2 = 16 - 1...
  13. C

    Max/min with partial derivatives

    well, from f_y, I can deduce that x=0 or yx^2 - x - 1 = 0. If x=0, from f_x, y= -2. If yx^2 - x - 1 = 0, y = (x+1)/(x^2) Subbing into f_x, -2(x^2 - 1)(2x) - 2((x+1)-x-1)(2x(x+1)/(x^2) - 1) = 0 -2(x^2 - 1)(2x) = 0 x(x^2 - 1) = 0 x = 0 (as above), x = 1 or x = -1 If x = 1, y = 2 If x = -1...
  14. C

    Maximizing Coffee Profits

    It's on the right track, but to finish it off, you should also apply the second derivative test for partial deriviatives.
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