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1d
comment Solution to the 1-D heat equation
I'm getting fussed at by the site moderator. This will be my last comment. Yes, I mean $u_x$.
1d
comment Solution to the 1-D heat equation
No, but setting the derivatives to zero on the boundaries does imply your integral. There might be several other artificial ways to satisfy your integral, like putting a "source" term on one boundary. Setting derivatives to zero is simplest.
1d
comment Solution to the 1-D heat equation
Your integral does imply mass conservation. Your boundary conditions $u(0,t)=u(L,t)=0$ guarantee that there will not be mass conservation. There is a contradiction.
1d
comment Solution to the 1-D heat equation
If you solve it with the boundary conditions you mentioned, you will absolutely not conserve mass because all the mass will slowly dribble out the ends of your domain. There is no way to fix this without changing the boundary conditions. Changing conditions so that the derivatives of $u$ are zero on the boundaries, or so that the boundary is periodic, would do it.
1d
comment Uncertainty in distance from uncertainty in coordinates
@witrup Thanks.
1d
asked Uncertainty in distance from uncertainty in coordinates
May
21
comment Prove that the following argument is valid
Hmmm, well, like I said, I'm not an expert. Good luck!
May
21
comment Prove that the following argument is valid
I'm not expert in formal logic at all, but P2 and P3 really bother me. Don't they imply $L\rightarrow\neg L$?
May
19
answered Help with calculating division with remainders on normal calculators.
May
8
comment What's the most efficient way to fit a surface to three or more points?
For each of your $(x,y)$ points, you need the corresponding value of $s$. And if you have three of them, you will not get the "best" fit, you will get the only fit.
May
8
answered Ortho projection of 3D points with a vector
May
4
comment limit of $\ln x + (x+1)/x$ as $x$ approaches $o$
No time to work up a rigorous proof, but $\ln x$ diverges more slowly than $1/x$, so the result is $\infty$.
May
1
answered optimization for the area of a garden
Apr
30
comment Calculating uncertainty in standard deviation
@Kyson I've looked it over. I don't see how I can use it. I'm admittedly not the sharpest tool in the shed sometimes. Any details you are thinking about will be most welcome.
Apr
30
comment Calculating uncertainty in standard deviation
@KYson I mean that the distribution has some value of standard deviation. I can get some approximation to that value by pulling a number of points out of it and taking their standard deviation. But the number that I get won't be the exact S.D. of the entire distribution. But surely, I am thinking, it must be good to within some "window". What is "the width of that window"?
Apr
30
asked Calculating uncertainty in standard deviation
Apr
23
answered Fourier Transform for Boundary Value Problems
Apr
16
revised How to determine if an equation represents a cubic spline?
correction
Apr
16
comment How to determine if an equation represents a cubic spline?
@jaska Whoops! LutzL is right! I forgot! You have to check the second derivative too.
Apr
16
comment How to determine if an equation represents a cubic spline?
Yes, the derivatives of both functions should be the same value at x=1. (And the values of the functions should also be the same at x=1.)