Recent content by Yegor

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    Graduate Differential equations and integal transforms

    Thank you very much for interesting information!
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    Graduate Differential equations and integal transforms

    Should i ask such questions in Homework Forum?! :confused: It's not a homework at all... just hoping that someone have more experience with such things...
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    Graduate Differential equations and integal transforms

    Differential equations and integral transforms Hi! I have some general questions on using integral transforms for solving differential equations. Also, I know that Fourier and Laplace transforms are useful means for solving linear ODE's and PDE's. 1. Are there cases, when one of them is...
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    Calculating Point Charge Potential at (0,0,0)

    Hallo! Homework Statement Consider electrostatic Potential of point charge at point (0,0,0) \phi = 1/r I'm trying to calculate \Delta\phi Homework Equations The Attempt at a Solution Actually it's not a difficult problem outside (0,0,0): \nabla\phi = -\frac{\vec r}{r^3} \Delta\phi = 0 But...
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    Where Does the Energy Go in a Capacitor Without Resistance?

    Thank you very much. As i understood, the model without resistance isn't really physical. With nonzero resistance everything is ok.
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    Where Does the Energy Go in a Capacitor Without Resistance?

    The capacitor of capacitance C is charged by battery (emf = E) (assume that there is no resistance). In the end charge of the capacitor Q = C*E; Work done by the battery W = Q*E=C*E^2. But The energy of charged capacitor is U = (C*E^2)/2. Work doesn't equals to stored energy. Where we lost...
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    Solving limit with algebraic tools

    Thank you very much, VietDao. Your approach is really very nice. But unfortunately i cannot use derivatives :cry: . Just algebra
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    Solving limit with algebraic tools

    So, i tried to get some more terms of \sin x expansion. Here is my result: \sin x = 2 \sin \frac{x}{2} \cos \frac{x}{2} = 2 \sin \frac{x}{2} (\cos \frac{x}{2} -1 +1) = -2 \sin \frac{x}{2} (1-\cos \frac{x}{2}) + 2\sin \frac{x}{2} = -4 \sin \frac{x}{2} (\sin \frac{x}{4})^2 +2\sin \frac{x}{2}...
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    Solving limit with algebraic tools

    Realy, nobody have any idea about initial problem?
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    Solving limit with algebraic tools

    Possibly, Benorin meant \lim_{x\rightarrow 0} \frac{\sin(x)}{x}=1, but i believe, that this can't help in solving initial problem. I have to use further terms of sinx series. \sin x = x - \frac{x^3}{3!}+... But how can i get them algebraically??
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    Solving limit with algebraic tools

    Hello! \lim_{x\rightarrow 0} \frac{-x(1 -\cos x)}{\sin x - x} I solved this limit using L'Hopital and expanding trigonometric functions to series. But i have to solve it using algebraic tools (without series). I don't know how to do it. \sin x - x looks difficult to deal with.
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    Undergrad Calc Moment of Inertia of Spinning Disc at Angle

    I think you aren't right here. Distance to the axis doesn't remains the same for each point (it doesn't equals the distance to the centre of disc, but shortest distance to the axis!). If you know I according to 3 orthogonal axis, then you can calculate I for each axis (through the same point)...
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    Graduate Why U is a State Function if W(adiabatic) Does Not Depend on State?

    Are state functions defined for entire thermodynamics or for certain processes? If last then it's possible to say that in adiabatic process work is state function.
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    Integrating sqrt(10z - z^2) using Trigonometric Substitution

    Last line isn't correct. it should be I= - \int \sqrt{t (10-t)} dt
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    Integrating sqrt(10z - z^2) using Trigonometric Substitution

    10z-z^2=5^2-(z-5)^2 Try z-5=5\cos{t}