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2d
comment What is the area of the shaded region of the rectangle?
What do the "2" and "3" mean? Are those the areas of the enclosed triangles?
Apr
27
comment How to find $\int \frac {sinh(lnx)} {x}$
$e^{-\ln{x}}=1/x$
Mar
24
comment Transforming points between two polar coordinate systems
You can certainly do the transformation, but it cannot be accomplished by a matrix. I think what you are doing is te way to go about it. You might take a look at how you can condense your operations instead of doing a laborious step-by-step process. But conceptually, I don't think you will find anything different from what you are already doing.
Mar
22
comment How to express elements of a first and second fundamental forms by their eigenvalues
I think more information is needed to answer the question. A simple diagonal matrix with the elements being the eigenvalues represents such a matrix ... in a particular coordinate system. Transforming to other systems requires alot more info.
Mar
16
comment Find the equilibria of the discrete dynamical system
You have a system of equations in two variables, $x$ and $y$. Just solve it for $x$ and $y$. Although, it does seem like there isn't going to be any "clean" solution. It's not going to be a typically "nice" solution to a textbook problem.
Mar
14
comment Frenet-Serret formulas in arbitrary dimensions
Sorry, I don't mean to be obtuse. And if you want to give up, I don't blame you. I understand $e^{\prime}_1\cdot e_j=0, j>2$, and I understand $e^{\prime}_2\cdot e_4=-e^{\prime}_4\cdot e_2$. For the life of me, I can't see why $e^{\prime}_2\cdot e_4 = 0$.
Mar
14
comment How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates
Seriously, seriously, get used to polar coords. You will suffer if you don't. I speak from experience.
Mar
14
comment Frenet-Serret formulas in arbitrary dimensions
I'm new at this. The paper you mention is beyond me right now.
Mar
14
comment Frenet-Serret formulas in arbitrary dimensions
OK, your expression for $e^{\prime}_j$ is exactly where my problem is. My understanding of the frame is such that you start with the various derivatives of the motion, and then perform a Gramm-Schmidt process to get the various $e$'s. And I don't see how that process implies $e^{\prime}_j=−κ_{j−1}e_{j−1}+κ_je_{j+1}$. I mean, I don't see a priori why $e^{\prime}_j$ for the general case can't have components of any number of the other vectors. Am I missing something obvious? Thanks for your help.
Mar
14
asked Frenet-Serret formulas in arbitrary dimensions
Mar
7
comment Converting from parts of a circle to polar coordinates
@Frank Vel The way I see it $x/4-x^2/4<y^2<1-x^2 \implies x/4+3x^2/4<y^2+x^2<1$
Mar
4
answered Converting from parts of a circle to polar coordinates
Mar
3
comment Describing a vector field
@Panphobia You seem to have gotten the idea, so I'll just say it more cleanly: The vectors point along circles and the magnitude of the vector decreases as $1/r$. I think that's probably what you need to say.
Mar
3
comment Describing a vector field
@Panphobia Well, crap, I read it wrong. You are right about the factor of $r$. The rest of what I said still holds. Your last comment is exactly right.
Mar
3
comment Finding the Velocity of a Particle after an Impact
In (2), you know $\theta$ so you can get $v_2$ immediately. This simplifies things alot. I didn't look in detail at your last equation, but you're definitely making a math error.
Mar
3
comment Describing a vector field
I think your calculation of $G$ is off by a factor of $r$. (Note that the original $G$ has no units, but your calculation of it has units $1/r$.) After that, just draw a circle, plot $G$ at a few points on the circle, and I think you'll see pretty clearly. I think they are getting at how $G$ relates to the circle.
Feb
18
awarded  Notable Question
Feb
6
awarded  Yearling
Feb
5
accepted Calculating uncertainty in standard deviation
Jan
19
answered A Simple Set Theory Question