Recent content by ad absurdum

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    Solving Integration Problem: \int_0^a x Sin^2\left(\frac{nx\pi}{a}\right) dx

    You need to use the identity \cos(2x) = 1 - 2\sin^2(x) to turn \sin^2(x) into a sum of things you know how to integrate (either directly or using integration by parts).
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    Deriving Conservation of Mass & Momentum for an Inviscid Compressible Gas

    Homework Statement Starting from the equations of conservation of mass and momentum for an inviscid compressible gas, \frac{\partial \rho}{\partial t} + \bigtriangledown . (\rho {\bf u}) = 0 \rho ( \frac{\partial {\bf u}}{\partial t} + ({\bf u}. \bigtriangledown){\bf u}) = \bigtriangledown...
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    Courses Cambridge Maths & Physics: Advice on Tripos & Courses

    I applied for maths with physics, and switched to straight maths a couple of weeks into my first term. The reason for this was that I really wasn't interested in doing any practicals. I didn't really get much of a chance to gauge the workload, but if your college makes you do all four of the...
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    Spiraling Inwards: Proving a Particle's Time to Reach a Fixed Point

    Homework Statement A particle P of mass m moves under the infulence of a central force of magnitude mkr^{-3} directed towards a fixed point O. Initially r=a and P has a velocity V perpendicular to OP, where V^2 < \frac{k}{a^2}. Prove that P spirals in towards O and reaches O in a time T =...
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