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    Derive Wirtinger derivatives

    Let \bar{z} = x+iy. We are given that x = \frac{z+\bar{z}}{2} & y = \frac{z-\bar{z}}{2i}. We are trying to derive \partial F/\partial\bar{z} = 1/2(\partial F/ \partial x + i \partial F/ \partial y), where F(x,y) is some function of two real variables. Using the chain rule I get \partial...
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    Initial Value Problem with Laplace Transforms

    Solve the following given y(0) = 0 & y'(0)=1: y′′+3y′+2y = u2(t), such that u2(t) is a heaviside step function Here's what I've got so far, =>s2Y(s)−sy(0)−y′(0) + 3sY(s)−3y(0) + 2Y(s)= exp(−2s)/s Y(s) = (exp(−2s) + s) / (s(s2+3s+2)) Y(s) = exp(−2s)/(s(s2+3s+2))* + 1/(s2+3s+2)** The...
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    Determine the indicated roots of the complex number

    Thanks everyone for your input. Much appreciated.
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    Determine the indicated roots of the complex number

    The answer in the back is actually +/-(sqrt 3 + i) / sqrt(2). The text doesn't specify how many roots to find, but it looks like two roots. I believe i've converted it to the latter form(k = 0), but I'm still unsure what more I need to do to get the roots.
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    Determine the indicated roots of the complex number

    [2(cos(pi/3)+isin(pi/3))]1/2 I simplified it to 21/2(cos(pi/6)+isin(pi/6)), but I have no idea what else to go to. Any tips would be very helpful, thx in advance
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    Linear Differential Problem(Pollutants into a lake)

    Hi, This is my problem: Consider a lake of constant volume V containing at time t an amount Q(t) of pollutant, evenly distributed throughout the lake with a concentration c(t), where c(t) = Q(t)/V . Assume that water containing a concentration k of pollutant enters the lake at a rate r...
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    Changing the order of a triple integration

    I'm given this definite integral: \int_0^{1}\int_{\sqrt{x}}^{1}\int_{0}^{1-y}f(x,y,z)dzdydx I need to change the order to dydxdz, but I'm stuck trying to get the limits of integration wrt y. \int_0^{1}\int_{x^2}^{0}\int_{}^{}f(x,y,z)dydzdx How do I find the limits of y?
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    Find the center of mass of a lamina

    That is a very good strategy I overlooked. Thanks so much.
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    Find the center of mass of a lamina

    The boundary of a lamina consists of the semicircles y=\sqrt{1-x^2} and y=\sqrt{4-x^2} together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin. I drew a graph that looks like...
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    Using polar coordinates to find the volume of a bounded solid

    I think that's the root of my problem. I found a http://answers.yahoo.com/question/index?qid=20080327174835AA36kOs" that's similar, but it doesn't show the work to get the integrand.
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    Using polar coordinates to find the volume of a bounded solid

    Using polar coordinates to find the volume of a bounded solid[Solved] I found the equation of the boundary circle by setting z to 4 in the paraboloid. Then I did some work to get polar coords: x^2+y^2 = 1 x^2+y^2 = r^2 1-x^2-y^2 = 1-r^2 Then I set up my integral as such...
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    Volume of Tetrahedron

    Thank you both! I'll definitely work on my latex once things settle down so that I don't cause so much confusion. And yes, in fact I add 24 to -168 instead of subtracting.
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    Volume of Tetrahedron

    Volume of Tetrahedron[Solved] My text book opts to integrate with respect to y before x(dydx vs dxdy), so I assumed that it would not affect the outcome. I set the upper and lower bounds of y, respectively, as y = 24 - 7x/4 (from 7x+4y=96) to y = x/4 (from x = 4y). For x I set it from...
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    How fast is the distance between the cars changing at this moment

    [Solved]How fast is the distance between the cars changing at this moment I'm in need of help with the last part (finding dz/dt). I'm sorry I don't know how to use latex. Let D refer to partial derivatives. This was my attempt best try: Given dz/dt = Dz/Dt*dx/d+ Dz/Dt*dy/dt and z...
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    Show that two lines(in 3D) are parallel, skew or intercept

    Well according to my calculator the first one intersects at (7,5,-3). But I couldn't get this on paper! When I solve for t and s, they end up as t=-3/2 and s=-4/3. It works fine for solving the x and y equations, but once I plug those into the z equations, it doesn't satisfy.
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    Show that two lines(in 3D) are parallel, skew or intercept

    http://img204.imageshack.us/img204/7130/screenshotxe.png [Broken] Hi, I was given this online assignment and this was one question I could not get. I know that two parallel lines parallel if their normal vectors' are scalar multiples of each other. And that if solving for t and s with two...
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