Reading: This material is scattered over many sections. Some
of those sections rehash what we have already talked about,
others derive the same result in multiple ways so you can
get a perspective for the differences. We have only time
to really cover some of this material, so I've skipped around.
The sections you should definitely read are:
Special Functions
Sections: 7.7-7.8 (Bessel Functions)
Sections: 7.9-7.10 (Other related special functions)
Eigenfunction Expensions
Sections: 8.3-8.4
Transforms
Sections: 10.1-10.2(motivation)
Sections: 10.3-10.4(computation) and 10.6.3
Sections: 10.5.1-2(Sine and Cosine Transforms)
Problems To Hand In:
Exercise: 7.7.3ab (variation of wave equation example from class).
Exercise: 7.7.6 (see also 7.7.1 which has an answer in the book)
Exercise: 7.7.9 part b) (heat eqn with bessel function).
Exercise: 7.8.2
Exercise: 8.4.1b
Exercise: 10.3.4.
Exercise: 10.3.5.
Exercise: 10.3.6.
Do the problem for 10.4.9 as follows:
Take the appropriate transform in the x-direction.
Find the general solution for the resulting ODE in y.
To solve for the coefficients c1 and c2 in the general
solution, read section 10.6.3 (lead up to equation (10.6.51).
You don't need to rewrite the inverse transform as a convolution,
though if you are interested, they do it in section 10.6.3.