Due Wednesday Feb. 25

Again on this assignment, you should employ computing resources and include plots to communicate your results.

This assignments includes the following problems from the text and 3 additional problems. The full assignments is available in PDF format.

Please download HW#4 by following this link.

Section 12.8 # 11, 13

Section 12.9 # 6, 15

Section 12.11 # 6

Due Wed. 2/11/09 (EDGE assignments should be received by 2PM Friday 11/13.)

Section 12.3 # 15, 16, 17, 19 (For #17 and 19, determine the first 3 frequencies and eigenfunctions/mode shapes and create an animation of the solution. For #19,  take the initial displacement to be f(x) = x^2*(1-x)^2. Note that, for the purposes of handing in hardcopy of your assignment, animation is replaced by a collection of frames using something like GraphicsGrid[ ].)

Section 12.5 # 10, 11, 17, 31, 32, 33 (Whenever possible, use computer algebra to help with – or at least verify – your results and include a plot of your solution.)

Due for all students by 2PM Tuesday Jan. 27. Note that there are a lot of problems on this assignment, so you have some extra time to work on it. The bulk of the material deals with Laplace Transforms, and a certain amount of practice is required to become a capable user (which should hopefully occur before the first exam on Friday, Jan. 30.)

1. Application of Fourier Transform to signal analysis:
a) Create a band limited spectrum by specifying an amplitude function that is zero beyond some maximum frequency, omega_o.
b) Apply the inverse Fourier Transform to construct the signal, f(t), associated with your spectrum.
c) Construct a list of regularly spaced sample values of the function. Make sure that the sample spacing is less than Pi/omega_o.
d) Show that adding up Sinc[ ] functions associated with the sample points accurately reproduces the signal, f(t).

In the text:
Section 6.1 # 9, 14, 29, 31, 34, 41, 47
Section 6.2 # 11, 12, 15, 18
Section 6.3 # 27, 32
Section 6.4 # 1, 4, 8 (Include a plot of the solutions.)

Due in class on Wed. 1/14. (EDGE students please make sure that we receive your work by Friday at 2PM.)

Section 11.4 # 2, 3, 11, 12
Section 11.6 # 9: Compute the Fourier Series and truncate to obtain trigonometric polynomials. Evaluate and plot the error in the truncated Fourier series as a function of the number of terms retained (i.e., plot E* vs. N). Also, pick a value of N and change the values of a_N and b_N. Plot the error as a function of a_N and b_N. Do your numerical results agree with the result that the Fourier coefficients provide the optimal approximation?