my intuition for differential forms is that in order to define integration you have to have linear data in order to approximate the area under the curve so that is why for instance the definition of differential forms are natural in terms of sections of the tangent bundle.
I like derivation definition the most I get the most feel
yes probably, it's from all I've seen (which isnt that much) an extremely elegant and useful theory, but not if they come out of nowhere and you've been introduced to manifolds 4 weeks earlier
Recently I was reader a paper where "for the convenience of the reader we will present here some proofs from [18], but note that the construction presented there is much more general" and then [18] are some unpublished notes that appear to not be available online...
I want to show that the sequence $a_n=\frac 1n -2^{-n}$ is decreasing. I have tried to show that $a_{n+1}-a_n<0$ and $\frac{a_{n+1}}{a_n}<1$ but inboth cases I faced difficulties to continue. Which way do you suggest to show that?
I am trying to integrate this:
$$\int_0^\infty\frac{ 1}{x^2} \, \mathrm d x$$
I was trying to convert it into a complex integral. But did not know how to proceed.
My original question is :
$$\int_0^\infty\frac{1-\cos x}{x^2}\, \mathrm dx$$.
Can someone give me a hint on how to proceed.
Thanks...
Since $f(z) = \frac{1-e^{iz}}{z^2}$ has no singularities in the region enclosed by the piecewise smooth curve $C$, does that mean $\int_{C} f(z)dz = 0$?
@AttractorNotStrangeAtAll as a side note to what ted said, for square integrable functions f,g, the integral of f*g is always finite, and this integral can be thought of as an extension of the usual dot product of two vectors - to functions, which are basically uncountable vectors
Yeah, I think it is...$f(z) = \frac{1-e^{iz}}{z^2}$, and $C$, which is described in the link, doesn't seem to contain any singularities of $f$, so I believe the integral over $C$ should be $0$.
Got a question. Note I know absolutely nothing about complex analysis. If $i$ is the imaginary unit, $t \in \mathbb{R}$, and $k$ is some positive integer, what are the necessary conditions for $$\int_{0}^{\infty}e^{-x[1 - i(t/k)]}\text{ d}x$$ to converge?
(Even better, I'd like to know what the relevant theorems are)
Got cussed out by a brat who has no idea how to ask a question on main :P
Rambling for five paragraphs about differential geometry. And the only question is a beginning multivariable calculus/linear algebra question about orthonormal bases. Ugh.
I am trying to integrate this:
$$\int_0^\infty\frac{ 1}{x^2} \, \mathrm d x$$
I was trying to convert it into a complex integral. But did not know how to proceed.
My original question is :
$$\int_0^\infty\frac{1-\cos x}{x^2}\, \mathrm dx$$.
Can someone give me a hint on how to proceed.
Thanks...
