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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.
Jan
12
revised Software for drawing geometry diagrams
Added working url link.
Jan
11
comment Error When Using Mathematica To Solve Differential Equation
@Szabolcs: \bigl \bigr, \biggl \biggr, \Bigl \Bigr, and \Biggl \Biggr and maybe others. You can click edit underneath the question to see the raw LaTeX code used, and play around with it to see how it changes below in the preview window pane. Just try not save any edits you make unless they are intended edits to make the questions better. This is the code generated directly by Mathematica when doing the following in the previous comment. \left\{\left\{s[t]\to 10 \text{Cos}\left[\sqrt{\frac{11}{2}} t\right]\right\}\right\}. Thanks
Jan
11
comment Error When Using Mathematica To Solve Differential Equation
@Szabolcs: I am getting the exact same output if that is what your inquiry is about, right? It's how did I get Out[2]= to look like that. What you do is 1) Highlight the math text of the output in your Mathematica user window and right click it. Next, 2) You will right click the highlighted area and choose copy as LaTeX. 3) Then just paste the code to where ever you need it to be. The only difference that I see from directly doing that and the one shown here in the question, is the sizing of constructs such as braces, brackets, and etc. This can be manually adjusted with commands such as:
Jan
5
comment Error When Using Mathematica To Solve Differential Equation
@J.M.: Thanks for that info.