
Fourier Series 9

Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4

Lecture1.5

Lecture1.6

Lecture1.7

Lecture1.8

Lecture1.9

Fourier Series Part 3
One that [onefifth]. I there it is of the five look of the seven It’s one seventh four c over pi so you start to see patterns emerge, okay? Now you could just write down [nine]. [Eleven] like you just write them all down, and you could have a very accurate [44] it expansion and now let’s plug in so this is the final step the final Enchilada okay, so I’m going to get rid of this because this was just demonstration We need that little space there Okay, here. We go [f] of x It’s approximately equal to its approximate because we’re not doing an infinite number of terms. We’re just doing a few Now we got all the b’s okay Sick you see it’s the sum All these terms are [going] so we’re just dealing with these beasts these b terms, so we’re just summing them up B14 C over Pi So [be] [one] and let’s just write it [out]. It’s going to be [B1] times the sine of n, pi x over L So n is 1 Pi is Pi and then L [is] pi so the pies are always cancels, so this is [suitabie] [be] [1] times a sine of x [and] this is the sine of 1 x isn’t it but We just make a note of that you’ll see why it matters So then this is plus b to beat walt all that all the even B’s went away times the sine of 3x be three times a sine of 3x Plus B. Five times the sine of 5x plus B seven times the sine of I Make it in just Bailey good okay. So now plugging in the first one for C over [Pi] YouTube recently gave us permission to go [to] [a] fifteen [minute], so hopefully we’re not there, but if so, we’ve got it Plus you probably need a bucket of popcorn for this [for] this damn problem Okay, so this is for C over three Pi C I don’t even see I know that I know the pattern now write for C over three Pi sine of three x plus Five C of it over no, no no [four] C Over five pot. What’s really frustrating is when you make a mistake at the very end and you have to redo this damn thing but Ain’t going to happen We’re on the ball here This time for C Or a step and Pi time to sign Then I make it in barely. I can barely see that so let me write that underneath right from One compact + 4 C 5 Pi times the sine 5x + That’s a plus plus 40 over seven Pi times the sine of Man, I don’t know if I made it in or not yeah You can see it. [I] think you can see it this last term I’m going to call it out to you all audibly [4C] over Seven PI times the sine of 7 [x4] C over Seven PI times the sine of 7 x there’s a [7x] in here is what’s supposed to be in there, okay? done Is that not a monster okay? So back to spiders practice? I try this one out? [there’s] there’s you need to try an even one out you need to try one and that works out You know odd and even it’s useful for modeling. It’s one of this to me This and Matrices to me is the most brilliant mathematical thing that’s ever come along this guy was just this is incredible also Terms of 40th at is take your calculator and graph it. So let’s see equal to [one] okay, let’s see either one and graph this thing and See what you come out with you will be it’s cool. It’s really really cool. So it’s going to do this number It’s really cool to see it when it happens. It’s going to it’s going to Cut it’ll come up, and then we’ll come over like this, and [it’ll] come down And come over like this, and it’ll come up and come over like this now come down like this It’s really cool and then let your let your x scale be pI over two So [you] know what what your you know you know that? It’s you know hitting where it’s supposed to hit just you can watch it Just in all I remember the first time I got one I was just like that’s cool. Okay I’m gonna step aside and give you a clearer screenshot you