The book for the class that I'm currently taking is "Introduction to Applied Mathematics" by Gilbert Strang. Things have been good with this class until this chapter. If you have used this book, you will understand what I mean when I say it is different. Things have been ok, because I've been understanding it. But I seriously need someone to hand hold me through an example. Here is one of the two worked examples on this material. (pg 278)(adsbygoogle = window.adsbygoogle || []).push({});

EXAMPLE 2[itex] u_0(\theta) = \theta,\,\,\,-\pi<\theta<\pi.[/itex]

The Fourier series for [itex] u_0 [/itex] was calculated in equation (12);

[tex]\theta = 2\left(\frac{\sin\theta}{1}-\frac{\sin 2\theta}{2}+\frac{\sin 3\theta}{3}- \ldots \right). [/tex]

Therefore the Fourier series (21) for [itex] u [/itex] is

[tex] u(r,\theta)=2\left(\frac{r \sin\theta}{1}-r^2 \frac{\sin2\theta}{2}+r^3 \frac{\sin3\theta}{3}-\ldots \right). [/tex]

On the circle [itex] u [/itex] has a sudden jump at [itex] \theta = \pi [/itex], but inside the circle that jump is gone. The powers [itex] r^k [/itex] damp the high frequencies andLaplace's equation always has smooth solutions.

If someone would please help me fill in the missing steps, I would be relieved.

I feel like someone has showed me: [tex] 5x^2 + 30x +2 =0[/tex] and asked me to solve it for [itex] x [/itex] but I've never heard of the quadratic equation, or completing the square :)

I mean yes it would be nice if I could figure out those "in between steps". But, it is not coming to me... and we are moving quickly into the next chapter. So I need to know this. Thank you.

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# Homework Help: Fourier Series - Will someone walk me through this

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