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1. ### Limit involving dirac delta distributions

Sorry I mean to evaulate: \lim_{x\to 0^{+}} \frac{\delta'(x)}{\delta''(x)}
2. ### Limit involving dirac delta distributions

Hey All, I am trying to evaluate the limit: \lim_{x\to 0^{+}} \frac{\delta''(x)}{\delta''(x)} Where \delta'(x) is the first derivative of the dirac distribution and \delta''(x) is the second derivative of the dirac distribution. I thought about the fact that this expression...
3. ### I think this is a dominated convergence theorem question

Thanks Mathman
4. ### I think this is a dominated convergence theorem question

Thanks mathman, I think I expressed the question wrong. I don't really care (for the purposes of this post) about when the expression will be zero, I am more interested in understanding what the mathematician was talking about with the theorem of dominated convergence. Lets say the function...
5. ### I think this is a dominated convergence theorem question

Hey All, I have the following integral expression: y = lim_{h\to0^{+}} \frac{1}{2\pi} \left\{\int^{\infty}_{-\infty} P(\omega)\left[e^{i\omega h} - 1 \right] \right\} \Bigg/ h And I am trying to understand when this expression will be zero. I was talking to a mathematician who said...
6. ### Is this integral possible to solve

Thanks for the help guys - can you briefly explain (or point me towards) why real roots are a problem ? is it something to do with branch points in the complex plane ?
7. ### Is this integral possible to solve

Hi I was wondering if anyone has seen this integral in a table, or indeed knows if it is possible to solve: \int^{\infty}_{-\infty} \frac{x^{2}}{ax^{4} + bx^{2} + c} every table I look at seems to only go up to the first power of x in the numerator Thanks, Thrillhouse
8. ### Conceptual Problem with Convolution Theorem

Thanks AlpehZero - I guess it always helps to go back to the fundamental definitions ...
9. ### Conceptual Problem with Convolution Theorem

Hi - I'm trying to work out the following convolution problem: I have the following integral: \int^{\infty}_{-\infty}p(x)U(x)e^{-i \omega x}dx Where p(x) is any real function which is always positive and U(x) is the step function Obviously this can easily be solved using the...
10. ### Fourier Transform of One-Sided Convolution

Hey Ray, yeah I've noticed that Laplace transform one, but I really need the Fourier transform of this one sided one. I was hoping that the heaviside function would kill the -ve bounds of my Fourier Transform so that it would look like a Laplace transform, but in order to do that I need to...
11. ### Fourier Transform of One-Sided Convolution

Hi, Can anyone tell me if there is a convolution theorem for the fourier transform of: \int^{t}_{0}f(t-\tau)g(\tau)d\tau I know the convolution theorem for the Fourier Transform of: \int^{\infty}_{-\infty}f(t-\tau)g(\tau)d\tau But I can't seem to find (or proove!) anything...
12. ### Asymptotic Form of an Integral

Hey: I have an integral of the form: \int^{\infty}_{-\infty}\frac{x(\omega)}{\sigma^{2} + \omega^{2}}d\omega I'm wondering if this integral is a candidate for asymptotic analysis. My rationale is that as omega increases to either positive infinity or negative infinity, the function being...
13. ### Surface integral with vector integrand

But the surface is a vector because its an orientated surface right (surface + direction) ? I mean when you do your surface integrals, you don't just define the surface, you define direction of the normal vector of the differential elements of the surface surface Supposing you have some...
14. ### Second Shifting Theorem for Fourier Transforms ?

Hi, I know from my the t shifting theorem that if I take the laplace transform of a function which is multiplied by a step function: \mathcal{L}\{f(t-a)U(t-a) \} = e^{as}F(s) Does this same rule apply for Fourier Transforms ? i.e. \mathcal{F}\{f(t-a)U(t-a) \} = e^{as}F(\omega)...
15. ### A convolution of a convolution

thanks pbandjay
16. ### A convolution of a convolution

as in: f*g = \int^{\infty}_{-\infty} f(\tau)g(t-\tau) d\tau what would h*(f*g) look like ? -Thrillhouse
17. ### A convolution of a convolution

Hi, can someone please give me an example of what a convolution of a convolution would look like ? Thanks
18. ### Where is the bridge between Calculus and Physics?

so your equation: V_{2} - V_{1} = \int E \cdot dl Is a consequence of the fundamental theorem of line integrals which you should of met in one of your previous calc courses. What it says is that if your vector field (in this case the electric field) can be written in terms of the...