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Lapsed engineer/scientist (now a patent practitioner) seeking to expand his math skills. Most of those skills lay in areas useful in optics such as sums & integrals (like the one below), complex analysis, differential equations, transforms, and data analysis.

My greatest hits page. (a work in progress)

"Wir müssen wissen, wir werden wissen." - David Hilbert

The picture on the left represents the integration region for the following integral of functions of finite support:

$$T(\mathbf{u}',\mathbf{u}'') = \int_{\mathbb{R}^2} d^2 \mathbf{\sigma} \; S(\mathbf{\sigma}) P(\mathbf{u}'+\mathbf{\sigma}) P^*(\mathbf{u}''+\mathbf{\sigma})$$


18h
answered All solutions of the recurrence relation
18h
revised Find the Fourier transform of $u(x) = \frac{x \cos(2x)}{(1+x^2)^2}$
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20h
revised Find the Fourier transform of $u(x) = \frac{x \cos(2x)}{(1+x^2)^2}$
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21h
revised Find the Fourier transform of $u(x) = \frac{x \cos(2x)}{(1+x^2)^2}$
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21h
answered Find the Fourier transform of $u(x) = \frac{x \cos(2x)}{(1+x^2)^2}$
23h
revised How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?
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1d
revised Calculate the laplace transform…
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1d
answered Calculate the laplace transform…
1d
comment Rotation of the integration contour through an angle
I think you mean $u=0$, right?
1d
comment Derivation of Simple Projectile Motion with Drag
An issue with generic drag equations: forces like drag are non-conservative and act only in opposition to the direction of motion. Thus, writing an equation like you do is only useful when you know the direction of motion is not changing (e.g., analyzing a falling object). Something like $-k |\mathbf{v}|$ in the equation may be closer to reality.
1d
comment Symmetry of function defined by integral
Felix, I thought about accepting this answer, but it seems a little off. Not that it's wrong - it is not - but that you had to evaluate the integral and cast it into an alternative form. The problem I have with this is that the symmetry is indeed palpable once you evaluate the integral - but the challenge was to avoid doing that in the first place. Maybe if you can show how to derive a similar form from the integral directly, I may accept.
2d
answered heat equation with perfectly insulated end
2d
awarded  Great Question
2d
revised Symmetry of function defined by integral
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2d
comment Evaluate $\displaystyle\int_{-\infty}^{\infty}\frac{dx}{(1+x^2)^2}$ using residue method
Do you know what contour integration in the complex plane is? If so, then tell us how you would start working the problem out.
Nov
26
answered Solving PDE by Laplace Transform
Nov
25
comment Help with inverse Laplace transform
@Eng_Boody: just plug the inverse transform (i.e., the Heaviside) into the LT expression; the LT then results from the integral.
Nov
25
revised Help with inverse Laplace transform
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Nov
25
answered Help with inverse Laplace transform
Nov
25
comment Fixing the closed form of $\sum_{k=1}^nk\sin^2(kx).$
@Fmonkey2001: That wasn't made clear to me. In fact, reading your problem again, it isn't clear what you want other than a solution verification, which in that case, why not have a different way of deriving the result?