pasmith's latest activity
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Ppasmith replied to the thread Undergrad 2nd order ODE's, variation of parameters and the notorious constraint.Thinking about it more closely, we want ##c_1y_1 + c_2y_2## to be a particular solution. But we're happy if it's only determined up to a...
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Ppasmith replied to the thread Undergrad 2nd order ODE's, variation of parameters and the notorious constraint.I think you have an error in the algebra. Substituting the ansatz and condition into the ODE, we should find $$\begin{split}...
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Ppasmith replied to the thread Polar integral.Any CAS which knows that for ##a \in \mathbb{R}##, ##(a^2)^{1/2} = |a|## should be able to get it right.
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Ppasmith replied to the thread Polar integral.Based on the sketch, it seems that ##\theta## is the angle of cylindrical polar coordinates, not spherical polar coordinates. I agree...
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Ppasmith replied to the thread Undergrad Proving that convexity implies second order derivative being positive.It's a bit confusing to take ##b < a##; usually we have ##a < b##. My approach would be to define $$ g : [0,1]\to\mathbb{R} : x \mapsto...
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Ppasmith replied to the thread Graduate How to Find Critical Points of function f(x,y,z).A Hessian matrix must be symmetric; this matrix is not. This is a consequence of the problem I noted in my earlier post: the vector...