Taylor Martin
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 May29 answered If $f$ and $g$ are integrable functions on $I=[a,b]$ and if $h(x):=\inf(f(x), g(x))$ for all $x \in I$, prove that $h$ is integrable at $I$. May14 comment Bound on uniform norm of convolution of $L^p$ functions Oh. I didn't even know that notation was still used! May13 comment Bound on uniform norm of convolution of $L^p$ functions Don't you need $p^{-1}+q^{-1}=u^{-1}+1$? May13 answered Diffuse equation-type PDE: Help me! May12 comment How do I convert the limit definition of differentiability to different variables? Because $h$ is just a displacement vector (from the point in question, $(x_{0},y_{0})$), and you send it to $0$. Being a vector, it has coordinates. Call them $(x,y)$, or anything you wish. May12 revised How do I convert the limit definition of differentiability to different variables? added 236 characters in body May12 answered How do I convert the limit definition of differentiability to different variables? May12 revised A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$ added 40 characters in body May12 revised A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$ added 195 characters in body May12 answered A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$ May12 answered Examine the convergence of $\left({\cos n\over n}\right)$ May9 answered Show that $f \equiv 0$ May9 comment Variation of parameters: $y''-y'-2y=4e^{-t}$ See extended answer above. May9 revised Variation of parameters: $y''-y'-2y=4e^{-t}$ added 658 characters in body May9 comment Variation of parameters: $y''-y'-2y=4e^{-t}$ Well isn't that the question of the day; have you even attempted to compute it on your own?! May9 comment Variation of parameters: $y''-y'-2y=4e^{-t}$ For example, $v_{1}$ (with my convention) is $-\int\frac{e^{2t}4e^{-t}}{3e^{t}}\;dt=-\frac{4}{3}\int\;dt=\frac{4}{3}t$. May9 comment Variation of parameters: $y''-y'-2y=4e^{-t}$ Yes. And just proclaiming you can't do it doesn't help us to help you. I don't understand what's so difficult here; you're just computing integrals at this point, something you should have had lots of practice in before taking your current ODE course. May9 comment Questions about surface integrals and an example problem What do you mean? It's just notation for integrals; you're not literally multiplying anything by $dS$. $\int_{S}(x+y)\;dS$ just means integrate $(x+y)$ over $S$ with respect to the surface measure $dS$. To reduce matters to an ordinary iterated Riemann integral, you parameterize the surface and pull back $S$ to the parameter domain $D$, and along the way $dS$ becomes $|\phi_{u}\times\phi_{v}|\;du\;dv$. This can all be made rigorous, and indeed, if you looked in your calculus text book you would find a sketch of the proof. May9 comment Variation of parameters: $y''-y'-2y=4e^{-t}$ Your answer is fine. It depends on what you take to be $y_{1}$ and $y_{2}$; permuting them in the definition of $W$ will only change the sign, since $W$ is a determinant. But once you decide on your labeling, you must be consistant with the definitions for $v_{1}$ and $v_{2}$ (see the derivation of $v_{1}$ and $v_{2}$ in your text book). May9 comment Variation of parameters: $y''-y'-2y=4e^{-t}$ $W[e^{-t},e^{2t}](t)=2e^{-t}e^{2t}-(-e^{-t}e^{2t})=2e^{t}+e^{t}=3e^{t}$.