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 Dec10 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. Nov25 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. Nov24 comment $2\times2$ matrices are not big enough @MarcvanLeeuwen: Rotation matrices don't commute in three dimensions. Nov15 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. Oct29 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. Oct28 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. Oct25 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. Oct25 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. Oct25 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 $x^2+x$? Oct25 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. Oct15 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. Oct14 comment How do we explain to students that division by a vector does not make sense? It certainly depends on what your multiplication is. Oct6 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. Oct5 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? Sep30 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! Sep29 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? Sep28 comment is it true that $\det(I+A)>0$ , if $\det(A)>0$? +1 This is the simplest example, I think. Sep26 comment How to show that the is a $1-1$ correspondence between real numbers and the set of points of a line in the Euclidean plane? I think the question is about the relationship between $\mathbb{R}$ as a set of numbers and the geometric notion of a line, but I could be wrong. Sep25 comment Why do we think of a vector as being the same as a differential operator? @GeorgesElencwajg: If you think that's the answer, then post it as so. But I still wonder: if there's no reason to make no distinction, why does the author make no distinction? Sep22 comment Simplify the expression. Isn't this needlessly complicated? Why not just substract exponents at the second equality, if you're going to do it later anyway?