Recent content by raxAdaam

@MisterX - I thought I posted a quick thank you for sharing your thoughts. I really appreciate your weighing into let me know I'm not alone in this sentiment :D.

@arildno thanks for your comment. I realize that they do not represent restrictions, I guess I just feel that they are **suggestive** of restrictions because (ISFAIA) it is unnecessary. I also just don't understand why he would bother with those details?

Hi - I was reading Adams' "Calculus: A Complete Course" (6th edition) and he offers the following proof that the gradient of a function: I'm just wondering why the emphasis on specifying the values of x(0) and y(0), or even the need to specify t = 0 in the last statement? If \mathbf{r} is...

Vector Calculus by P.C. Matthews has an awesome chapter on index notation. I struggled with the notation enormously when it was tangentially introduced during and E&M course because neither the teacher nor the textbook provided sufficient information (for me) or any basic practice problems...

Thanks Dick - don't know why I missed that; guess I got disoriented in the semantics. Thanks for clarifying it explicitly :D.

Sorry "/= 1,2" is meant as "not equal to 1, 2" which, as HallsofIvy pointed out, is not proven.

So then how *can* you show that (A-cI) **is** invertible when c /= 1, 2?

Interesting, and this tends to be the case only for rational exponents? So were I to factor the expression in terms of an integer exponent, I would get the entire graph? How come these programs don't account for this method? Wouldn't it be relatively simple to include the other half of the...

When I plot y = 3x^{\frac{4}{3}}-\frac{3}{32}x^{\frac{2}{3}}, I get: https://dl.dropbox.com/u/5653705/pfgraph1.png but I don't see any reason for the domain to be restricted to x > 0 . There is only a cubic root, which is well defined for negative numbers ... I've tried on a few...

Any thoughts or clarifications on this? Am very keen to understand what's happening here ...

i.e. dA = 2\pi x~dx? So if it was possible to express the circumference of an ellipse strictly in terms of x, then we could do the same? (not sure 'bout the \Delta r above ... did you means \Delta x?)

alright - I see what you mean, now - how does this come to bare on the area to circumference issue? Perhaps the more relevant question is why the derivative of the area of the circle is equal to it's circumference ... thanks in advance!

I managed to answer the second question (I think / I hope!) & thought I'd post it in case anyone was curious. The first term w_y = \frac{\partial w}{\partial y} is just the usual partial, as mentioned above. Now the significance of the second term becomes clearer if one writes out the...

I think the problem is that you are taking interpretations of the derivative and the integral (which are inverse operations) for those things, themselves. Integrals can be understood as the area under a curve, but that doesn't mean that they are the area under the curve. For example, if you...

Could you clarify what you mean by this? What is the visual - where is the gap / thickness?