UnkleRhaukus
  • UnkleRhaukus
\(f(x)\) as a sine series
Differential Equations
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
UnkleRhaukus
  • UnkleRhaukus
\[ \qquad\text{\(f(x)\) as a sine series} \begin{equation*} % f(x) f(x)=1,\qquad0
UnkleRhaukus
  • UnkleRhaukus
\[\begin{equation*} % g(x) g(x)= \begin{cases} 1,&0
UnkleRhaukus
  • UnkleRhaukus
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experimentX
  • experimentX
just change L to pi http://mathworld.wolfram.com/FourierSeriesSquareWave.html
UnkleRhaukus
  • UnkleRhaukus
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experimentX
  • experimentX
you got the opposite one .. shift the period by +pi
UnkleRhaukus
  • UnkleRhaukus
where did i go wrong?
experimentX
  • experimentX
don't know .. don't have much time right now!! but i often use that link as reference!!
experimentX
  • experimentX
sin(nx) is not even .. get rid of that minus
experimentX
  • experimentX
i'll see later!!
UnkleRhaukus
  • UnkleRhaukus
why does (4) on that link have a sin^2 term?
UnkleRhaukus
  • UnkleRhaukus
ah i found my mistake
UnkleRhaukus
  • UnkleRhaukus
\[\begin{align*} % b_n b_n&=\frac1\pi\int\limits_{-\pi}^{\pi} g(x)\sin(n x)\,\text dx\\ &=\frac2\pi\int\limits_0^\pi \sin(n x)\,\text dx\qquad\text{even integrand}\\ &=\frac2\pi\left(\frac{-\cos(n x)}{n}\right)\Big|_0^\pi\\ &=\frac2\pi\left(\frac{\cos(0)-\cos(n\pi )}{n}\right)\\ &=\frac2{\pi}\left(\frac{1-(-1)^n}{n}\right)\\ \end{align*}\]
UnkleRhaukus
  • UnkleRhaukus
\begin{align*} S(x)&=\frac2\pi\sum\limits_{n=1}^\infty\left(\frac{1-(-1)^n}{n}\right)\sin(nx)\\ &=\frac4\pi\sum\limits_{n=1,3,5,\dots}^\infty\frac{\sin(nx)}{n}\\ &=\frac4\pi\sum\limits_{r=1}^\infty\frac{\sin\big((2r-1)x\big)}{2r-1} \end{align*}
UnkleRhaukus
  • UnkleRhaukus
just a minus sign
UnkleRhaukus
  • UnkleRhaukus
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anonymous
  • anonymous
anonymous
  • anonymous
guy please help me with this. This is impossible tough for me
UnkleRhaukus
  • UnkleRhaukus
i havent studies solving PDEs yet sorry @Echdip

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