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Nov
4
comment Monotonicity of the function in some near interval of a local maximum critical point
@iMath If that is your definition then a constant function, e.g. $f(x) = 5$ has a local maximum at every point (since there are no nearby values greater than $5$) but it's not increasing or decreasing (depending on your definition of increasing and decreasing).
Nov
3
answered Monotonicity of the function in some near interval of a local maximum critical point
Sep
30
awarded  Explainer
Sep
26
revised differentiating a function of a function $w=\sqrt{u^2+v^2}$
This is not a question about differential equations - retagged.
Sep
26
suggested suggested edit on differentiating a function of a function $w=\sqrt{u^2+v^2}$
Sep
5
awarded  Nice Answer
Aug
4
comment Why is $f(x)=\sin (2x-\pi)$ the same as $g(x)=-\sin(2x)$?
@user50224 Look at my comment on your original posting.
Aug
4
comment Why is $f(x)=\sin (2x-\pi)$ the same as $g(x)=-\sin(2x)$?
Step E: If you move $\sin(2x)$ by $\pi$ you get $\sin(2(x - \pi)) = \sin(2x - 2\pi) = \sin(2x)$. What you have actually done is moved it right by $\pi/2$ which is only half a period, hence the negative.
Jun
13
comment how do we interpret this integral from polar co-ordinates
@DavidH For what it's worth, I'm pretty sure he wants your interpretation of the integral.
Jun
13
comment how do we interpret this integral from polar co-ordinates
@DavidH Indeed. I did ask in the comments what he intended but he was adamant they were the same $r$.
Jun
13
answered how do we interpret this integral from polar co-ordinates
Jun
13
comment how do we interpret this integral from polar co-ordinates
Should this really be $dr$?(and not $ds$?)
May
12
comment Numerical one-step method: initial value and non consistent method
I think your explanation is good.
Apr
29
comment How can I show that ~ is an equivalence relation such that $x$~$y$ if there is a continuous path in $M$ from $x$ to $y$?
@1950RobertLewis I understand he's not a great guy, but he makes great tools. My username should really be "in_wolfram_alpha_we_trust"
Apr
29
comment How can I show that ~ is an equivalence relation such that $x$~$y$ if there is a continuous path in $M$ from $x$ to $y$?
@1950RobertLewis Who would you have me follow? :P
Apr
29
comment How can I show that ~ is an equivalence relation such that $x$~$y$ if there is a continuous path in $M$ from $x$ to $y$?
What is the definition of an equivalence relation? What properties should it satisfy? How can we show that this relation satisfies these properties?
Apr
25
revised Explanation and Proof of the fourth order Runge-Kutta method
Minor edits.
Apr
8
comment Second order Diff. Equation
Yeah, I filled in the details. It looks like that integral doesn't have a solution in terms of elementary functions. This is (I think) the best we can do.
Apr
8
revised Second order Diff. Equation
added 417 characters in body
Apr
7
answered Second order Diff. Equation