Recent content by elimenohpee

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    Engineering What does it takes to be a physicist compared to an engineer?

    If you want to be an engineer and physicist, you should consider electrical engineering. A lot of schools offer a double major in physics and ee, since a lot of the topics are similar. Plus with ee, you can get into solid state theory which really combines physics, engineering, and chemistry...
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    Residue theorem and laurent expansion

    Homework Statement I need to calculate the residue of a function at infinity. My teacher does this by expanding the function in a laurent expansion and deduces the value from that. That seems much harder than it needs to be. For example, in the notes he calculates the residue at infinity...
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    Evaluate Integral: \frac{16cos^{2}x}{5-4cosx}

    GAHHHHHH. Why didn't I see that! That is perfect, thank you so much. I understand completely where I went wrong. Have a great night!
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    Evaluate Integral: \frac{16cos^{2}x}{5-4cosx}

    can anyone else offer any insight?
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    Evaluate Integral: \frac{16cos^{2}x}{5-4cosx}

    Here is a calculation of the residue at z=0.5 http://www.wolframalpha.com/input/?i=residue+4%28z%2Bz^-1%29^2%2F%28-i%28z-2%29%282z-1%29%29+at+z%3D0.5 Here is the integral evaluated http://www.wolframalpha.com/input/?i=integrate+16cos^2+x+dx%2F%285-4cosx%29+from+0+to+pi
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    Evaluate Integral: \frac{16cos^{2}x}{5-4cosx}

    semi circle of radius 1. If you get i in the numerator, when you evaluate the contour integral, wouldn't that give you a negative area? I = 2*i*pi*residue = 2i pi*(25i/3)= -50pi/3
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    Evaluate Integral: \frac{16cos^{2}x}{5-4cosx}

    Some how the residue should be 5/3i but I'm getting 25/3i
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    Evaluate Integral: \frac{16cos^{2}x}{5-4cosx}

    I do, but there is also the factor of i*z from the change of variable in the differential term. So I factor that through the denominator, and it gives me (5z - 2z^2 -2) which factors to (z-2)(2z-1) The problem has to be with the residue, as that is the only residue which makes up the contour...
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    Evaluate Integral: \frac{16cos^{2}x}{5-4cosx}

    Homework Statement Use the residue theorem to evaluate: \int^{\pi}_{0}\frac{16cos^{2}xdx}{5-4cosx}The Attempt at a Solution I rewrote the integral with the substitutions z=e^{ix} dx = \frac{dz}{iz} cosx = 0.5(z+z^{-1}) cos^{2}x = 0.25(z+z^{-1})^{2} I throw all that in, convert the...
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    Developing a formula from cube equation

    wow, sorry I see now. Forgive what I just wrote, it is late and I wasn't thinking correctly. When I multiply out, I get: x^{3} -x^{2}(r_{1}+r_{2}+r_{3}) + x(r_{1}r_{2}+r_{1}r_{3}+r_{2}r_{3}) -r_{1}r_{2}r_{3}=0 then you can equate coefficients with the original cubic expression to get...
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    Developing a formula from cube equation

    Is that really all I need to do? I mean when I multiply it out, I get: x^{3}-cx^{2}-bx^{2}-ax^{2}+bcx+acx+abx-abc=0 The question says to develop formulae, all three formulas are within this equation...is there anything else I can really say here? lol
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    Developing a formula from cube equation

    Homework Statement Given that the equation x^{3} + ax^{2} + bx + c = 0 has the roots r_{1}, r_{2}, r_{3}, develop formulae for r_{1} + r_{2} + r_{3}, r_{1}r_{2}+r_{1}r_{3}+r_{2}r_{3}, r_{1}r_{2}r_{3} Homework Equations The Attempt at a Solution Not really sure where to...
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    Calculating Circle of Convergence for f(z) = (3z+1)/(15+2z-z^{2}) at z=1

    Thank you for the help once again.
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    Calculating Circle of Convergence for f(z) = (3z+1)/(15+2z-z^{2}) at z=1

    Before I type all of my work up, I get the convergence to be |z-1|< 4 ... if that's not right I'm lost lol.
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    Calculating Circle of Convergence for f(z) = (3z+1)/(15+2z-z^{2}) at z=1

    ahhhhhh..ok I got it now. Thank you! I will do that and repost to see if I get the right circle of convergence. Thanks :)