A community for students.
Here's the question you clicked on:
 0 viewing

This Question is Closed

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \qquad\text{\(f(x)\) as a sine series} \begin{equation*} % f(x) f(x)=1,\qquad0<x<\pi \end{equation*}\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\begin{equation*} % g(x) g(x)= \begin{cases} 1,&0<x<\pi\\ 1,&\pi<x<0 \end{cases}\qquad\text{odd extension of \(f(x)\)} \end{equation*}\] \begin{equation*} % a_0, a_n a_0=a_n=0\qquad\text{odd function} \end{equation*} \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*} \begin{align*} S(x)&=\frac2\pi\sum\limits_{n=1}^\infty\left(\frac{1(1)^n}{n}\right)\sin(nx)\\ &=\frac2\pi\sum\limits_{n=1,3,5,\dots}^\infty\left(\frac{2}{n}\right)\sin(nx)\\ &=\frac4\pi\sum\limits_{r=1}^\infty\frac{\sin\big((2r1)x\big)}{2r1} \end{align*}

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0just change L to pi http://mathworld.wolfram.com/FourierSeriesSquareWave.html

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0you got the opposite one .. shift the period by +pi

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0where did i go wrong?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0don't know .. don't have much time right now!! but i often use that link as reference!!

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0sin(nx) is not even .. get rid of that minus

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0why does (4) on that link have a sin^2 term?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0ah i found my mistake

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\begin{align*} % b_n b_n&=\frac1\pi\int\limits_{\pi}^{\pi} g(x)\sin(n x)\,\text dx\\ &=\frac2\pi\int\limits_0^\pi \sin(n x)\,\text dx\qquad\text{even integrand}\\ &=\frac2\pi\left(\frac{\cos(n x)}{n}\right)\Big_0^\pi\\ &=\frac2\pi\left(\frac{\cos(0)\cos(n\pi )}{n}\right)\\ &=\frac2{\pi}\left(\frac{1(1)^n}{n}\right)\\ \end{align*}\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\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((2r1)x\big)}{2r1} \end{align*}

Echdip
 2 years ago
Best ResponseYou've already chosen the best response.0guy please help me with this. This is impossible tough for me

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0i havent studies solving PDEs yet sorry @Echdip
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.