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Jan
1
comment Is this a solution to the indefinite integral of $e^{-x^2}$?
This is a nice idea, but I'm sorry to tell you that there's proof that there is no elementary formula for the integral. If you're okay with a series, just expand $ e^{-x^2} $ and integrate term by term.
Dec
13
comment Can integration get the real value of $\pi$?
@user3015600: You could, in principle, get $\pi$ with infinite precision. If you want any digit of the decimal expansion of $\pi$, there's a zillion formulas that you can use to get it. The problem is that we can never know all of them, not because math doesn't work, but simply because there's infinitely many of them and we don't have infinite time.
Dec
10
comment Explain complex numbers
Also, I think this is a duplicate: math.stackexchange.com/questions/251665/…
Dec
10
comment Explain complex numbers
@tandberg: You can't always explain something at a level the other person can understand. If your cousin is familiar with the plane and a bit of analytic geometry, you can make the connection there. Otherwise, I'm not sure.
Nov
25
comment $2\times2$ matrices are not big enough
@MarcvanLeeuwen: The reason I made my comment is that yours seemed to imply that this isn't a very good example because it's not evident how to define a rotation matrix for $n > 2$ dimensions. I just wanted to make clear that $3$-dimensional rotation matrices are easy to define and don't commute, that's all.
Nov
24
comment $2\times2$ matrices are not big enough
@MarcvanLeeuwen: Rotation matrices don't commute in three dimensions.
Nov
15
comment Solving $y'' + (ax+b)y = 0$
Side note; how do I make the expression for $\phi(k)$ look nice? The symbols look extremely small to me.
Oct
29
comment can not find the proof that logarithms are the inverse of exponentials
What's your definition of both? People usually define one of those to be the inverse of the other.
Oct
28
comment What situations/models require calculating the area under a curve?
Are you asking specifically about finding the area below a curve, or about integrating in general? Because there is an endless list of uses for the latter.
Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
I just clicked "edit" and then "roll back" on the first revision, if that's what you're asking.
Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
I rolled the question back to what it was originally. You should probably add a disclaimer to your answer so people don't start downvoting you.
Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
Also, what sort of course are you following that you can talk about minimal surfaces but don't know the derivative of $x^2+x$?
Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
Please don't change your question to something else. If you have a new question, ask a new question.
Oct
15
comment What's the integral of $\frac{-4x}{1+2x}$?
Constants don't matter when doing integrals. In this case, the $-1$ gets absorbed into the $+C$ that you should have put when doing the integral.
Oct
14
comment How do we explain to students that division by a vector does not make sense?
It certainly depends on what your multiplication is.
Oct
6
comment How to tell if multivariable function is odd?
You just do. It's something you get used to after a while. After all, it's usually pretty easy to tell at a glance whether a function is odd.
Oct
5
comment Let $f,g$ be two distinct functions from $[0,1]$ to $(0, +\infty)$ such that $\int_{0}^{1} g = \int_{0}^{1} f $.
Are those powers or derivatives?
Sep
30
comment Why do we think of a vector as being the same as a differential operator?
I think I like your answer the most, but I'll wait a bit longer just in case another one pops up. Thanks!
Sep
29
comment Why do we think of a vector as being the same as a differential operator?
Why is it the only sensible definition? If I have a point $p \in M$ and an open set $U \ni p$ with local coordinates $\phi: U \to \mathbb{R}^n$, then I can choose (for example) the standard basis of $\mathbb{R}^n$, and if I want to use another coordinate system, the vectors transform as dictated by the Jacobian, so my basis is well-defined regardless of the coordinates. Isn't this right?
Sep
28
comment is it true that $\det(I+A)>0$ , if $\det(A)>0$?
+1 This is the simplest example, I think.