Homework 10, due December 1, 2010.

[goodwine]

Reading: all of chapter 11 and chapter 12, sections 1-3.

Exercises: 11.12, 11.17. 11.19, 11.21, 12.1 (number 8 only) and 12.2 (number 7 only).

[cdiberna]

Hi Prof. Goodwine,

I was trying to to do problem 11.17 and I was having trouble because the equations in the book do not account for an initial velocity profile. Are the equations for c and d supposed to have g instead of f in there? Thanks.

[goodwine]

Hi Prof. Goodwine,

I was trying to to do problem 11.17 and I was having trouble because the equations in the book do not account for an initial velocity profile. Are the equations for c and d supposed to have g instead of f in there? Thanks.

I don't have the book with me bot g should definitely be in the equations fou the Fourier coefficients. The velocity should affect the sine coefficients since those become cosines when differentiated.

[sprender]

For problem 11.17, how can we incorporate J_m into our code if it is dependent on a table of values in the book? Do we need to enter a portion of this table into the code and only include sums over the range of the table that we include? Also, is it possible to plot in 3D polar coordinates in Matlab and if so, how?

[goodwine]

For problem 11.17, how can we incorporate J_m into our code if it is dependent on a table of values in the book? Do we need to enter a portion of this table into the code and only include sums over the range of the table that we include? Also, is it possible to plot in 3D polar coordinates in Matlab and if so, how?

The boundary conditions will force the Bessel function to be zero at certain points. In class (and in the book) z_{m,n} stands for the nth zero of J_m (maybe m and n are the other way around). It plays the same role at 2 pi for the sine and cosine functions. The best you can do to write a solution is to use z_{m,n}. If you are plotting something, then you need to make a vector or matrix of those values.

I don't know how to 3-D polar plots in Matlab, although I suspect there is a way.

[goodwine]

Someone sent the following link to me, which you may find helpful to compute the zeros for the Bessel functions:

http://www.mathworks.com/matlabcentral/ ... hange/6794