Department of Mathematics

Math 600: Topics in Mathematical Computing

Project

Your assignment is to make a fit to a data set using your choice of Matlab or Maple, and then to write about the results.

  1. There is a data set called watemp.txt in the /users/M300 directory. The data describe temperatures in Washington State from 1931 to 2000. The first column represents the year, the second the average temperature (in Fahrenheit) for January, the third the temperature for February, and so on, the 13th column representing the average temperature for December. The last column is an an annual average temperature for Washington. The data were found at the NOAA web site.
  2. Write a script or worksheet to solve the normal equations for a specified column of this data file, and to plot and label the figure you must generate below in part 4. As graduate students, you should solve the normal equations in a stable way.
  3. Fit a linear polynomial at+b to the data in the last column, using the least squares method we illustrated in class. Make also a fit using a quadratic polynomial at2+bt+c.
  4. Compute the norm of the error vector for each of the approximations in the previous step.
  5. Produce one plot of the year for the data against the temperature, showing the data as points, and the two fits as continuous curves. Make sure the axes are labelled and the plot has a title.
  6. Save the plot as a JPEG file.
  7. Write a LaTeX document describing the mathematics behind the script you wrote, including the text of the script or worksheet in a verbatim environment in an appendix to the document.
  8. Make a second section in your document giving a discussion and conclusions concerning trends in temperature in Washington State. Include the JPEG plot you created in the section. Note that this will only work for a PDF version of the document. Draw conclusions based on the coefficients of the curves you fitted. This section will be short.
  9. Mail the completed TeX file and all associated scripts and figures to the instructor by the last day of the term.
  10. You may use Octave if you like. Just let the instructor know.

Welcome to Math 600, Topics in Mathematics Computing.

This class will meet Mondays at 3:10. in Neill 120.

We will cover Matlab (including gui design) through the end of the semester. The project has been posted.



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