18.311 MIT (Spring 2011).
Rodolfo R. Rosales (MIT, Math. Dept., 2-337, Cambridge, MA 02139).
Date: May 2, 2011.

Problem Set # 07 for 18.311
Due: Last day of lectures.
Turn it in before 3:30 PM, in the box provided in Room 2-108.

IMPORTANT: The Regular the Special Problems must be stapled in
TWO SEPARATE packages, each with your FULL NAME clearly spelled.

% =====================================================================
Regular problem set.
  SMFS03. Compute derivatives using the FFT.
  Note that you can use this problem as a check that your answer
  for the special problem below is correct. Derivatives of smooth
  functions computed using FFT's are very accurate. If this does
  not happen, either you have a programming error, or your answer
  to SMFS02 is not correct. Go back and fix it.

Special problem set.
  SMFS02. Formula to approximate the derivative using the FFT.
  WARNING: Since you can check your answer to this problem using
           SMFS03, I stress that I expect an answer to this problem
  which is justified. No trial and error, or just stating the answer
  without explanation. This is not acceptable as an answer.

% =====================================================================
The problems above are from the: Spectral Methods and Fourier Series
notes --- posted in the 18.311 web page.
% =====================================================================
EOF