Bill Goodwine's Courses

1. Compute the Fourier series for
   • 
   where
   • 
   Plot f(x) and the first several terms of the series on the same graph.
2. Compute the Fourier series for
   • 
   where
   • 
   Plot f(x) and the first several terms of the series on the same graph.
3. Determine the solution to
   • 
   where
   • 
   and
   • 
   Plot the solution for t=0 and several other times to clearly demonstrate the nature of the solution.
4. Determine the solution to
   • 
   where
   • 
   and
   • 
5. Determine the solution to the wave equation where
   • 
   Plot the solution for t=0 and several other times to clearly demonstrate the nature of the solution.
   
   Extra credit: make a movie of the solution.
6. Determine the solution to the wave equation where
   • 
7. Determine the solution to
   • 
   where
   • 
   and
   • 
8. By assuming u(x,y)=X(x)Y(y), determine the solution to
   • 
   where
   • 
   Plot an approximation to the solution by using the first few terms in the series representation of the solution.
9. Consider the famous Lorenz equations
   • 
   where
   • 
   1. Use the second order Taylor series method to determine an approximate numerical solution to these equations for the time range t=0 to t=50. Submit a 3D plot of (x,y,z). Be sure to experiment with the time step to ensure that your solution is accurate. The Matlab plot3() function will probably be useful. A quick google search will probably give you an idea of what the plot should look like.
   2. Use Matlab's ode45() to compute an approximate solution and plot the result. Compare it with your plot from the first part of this problem.

avalenzu wrote:When you ask us to "Plot f(x) and the first several terms of the series on the same graph," which of the following (if either) do you mean?

A)
Plot 1: f(x)
Plot 2: term1 + term2 + term3 + term4

or

B)
Plot 1: f(x)
Plot 2: term1
Plot 3: term2
Plot 4: term3
Plot 5: term4

colinheye wrote:Is the very first coefficient on problem 7 an 'a' or an alpha?

colinheye wrote:Do we need to plot the different u(x,t) plots as well as a movie? How do you want us to get the movie file to you?

colinheye wrote:Do we need to plot the different u(x,t) plots as well as a movie? How do you want us to get the movie file to you?