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visits member for 3 years, 8 months
seen Sep 2 '13 at 3:01

Apr
19
comment Definition of Sinc function
@J.M.: What do you mean by using one name for two different functions? I'm more so used to the normalized form.
Apr
19
asked Definition of Sinc function
Mar
25
comment Integral Transform
@Mathlover: where does the $e^t$ go, that's on the outside of the integral on the RHS of the equation?
Mar
24
comment Integral Transform
@Tpofofn: Thanks, I realized that. But I need the function $w(t)$ to determine the output to another system with $w(t)$ being the input. This is why I needed to integrate or use properties to transform $W(f) \leftrightarrow w(t)$.
Mar
23
comment Integral Transform
@Mathlover: Ah hah, I knew that integral looked familiar. I do not have a book handy, but is this a transform pair I believe or property? I just remember seeing it sometime ago, but haven't used it before. Which now makes more sense in terms of what functional constructs that has infinite amplitude, such as the dirac. Thank You!
Mar
23
comment Integral Transform
@Mathlover: I didn't get what you meant by that. It would be in terms of $f$ correct because its indefinite and its whats the independent variable is for that case, right? So would our $w(t) = e^t\int_{-\infty}^{\infty} j\pi f e^{j2\pi ft} df$?
Mar
23
comment Integral Transform
@Mathlover: Exactly is what I get. I had done: $\frac{d}{dt}(w(t)e^t)=\frac{d}{dt}(\int \! \frac{j\pi f}{1+j2\pi f}e^{(j2\pi f+1)t} df)=\frac{e^{t+2 i \pi f t} (2 \pi f t+i)}{4 \pi t^2}$, because I know the integral would not converge, but when doing: $\frac{d}{dt}(w(t)e^t)=\frac{d}{dt}(\int_{-\infty}^{\infty} \! \frac{j\pi f}{1+j2\pi f}e^{(j2\pi f+1)t} df)$, it equal to what you have. So, for this last integral equation, this would be what $w(t)$ is? That's pretty interesting, for it to be in terms of a definite integral.
Mar
23
comment Integral Transform
@Mathlover: Thanks. So when doing this, I get for the right hand side before evaluating the limits is: $\frac{e^{t+2 i \pi f t} (2 \pi f t+i)}{4 \pi t^2}$. Now, plugging in limits, the integral will not converge on $[-\infty,\infty]\,$. How do we go from here to fully obtain the inverse of $W(f)$?
Mar
23
comment Integral Transform
@Tpofofn: Thanks, I just realized I did not need to find the inverse to get $w_1(t)$ because it was only asking for the frequency spectrum. But, how would I find the inverse of $W(f)$ to get what $w(t)$ is. Either using the definition which I started, or transform properties. I managed to get this from using the properties but not sure if it is correct: $w(t)= 1/2e^{-t}\frac{\mathrm{d}w}{\mathrm{d}t} u(t)\,$ where $u(t)$ is the unit step function.
Mar
23
asked Integral Transform
Mar
22
accepted Computing Coefficients of Complex Form Fourier Series
Mar
20
awarded  Yearling
Mar
5
asked Computing Coefficients of Complex Form Fourier Series
Feb
27
comment Nice proofs of $\zeta(4) = \pi^4/90$?
I wondering what does the $\zeta$ represent? Is that of any significance or just a variable?
Feb
18
accepted Sifting out Solutions to Differential Equations
Feb
18
comment Sifting out Solutions to Differential Equations
Hey Julian, This is a really well thought out response and helpful to know for future reference and work/research. Thank You.
Feb
17
asked Sifting out Solutions to Differential Equations
Jan
13
accepted Error When Using Mathematica To Solve Differential Equation
Jan
13
revised Calculate the unknown
added 4 characters in body
Jan
12
revised Software for drawing geometry diagrams
Added a url link.