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This homework is meant as review for the second-chance exam to be held Nov 26. It is due Thursday Nov 14th in lecture.

Review topics

• fprintf: formatted printing function
• plotting: plot, semilogy, semilogx, loglog, contour, mesh
• loops: for and while
• anonymous functions: defining and using
• solving equations: with fzero or newtonsearch

Problem 1: Write a Matlab function named farenheit2celsius that converts degrees Farenheit to degrees Celsius, according to the formula . Write the function in a file farenheit2celsius.m.

Problem 2: Write a for-loop that prints a Farenheit to Celsius conversion table for values of F between -10 and 120 degrees, in increments of 10 degrees F. The output should look something like this:

   0  F == -17.8 C
   10 F == -12.2 C

etc. Hint: use fprintf with a formatting codes %3d and %6.1f to get the numbers to line up nicely. That's three spaces for the integer F numbers, and six spaces for the floating-point C numbers, with 1 digit after the decimal point.

Problem 3: Make a plot of C versus F over the range -50 <= F <= 212. Put symbols on the line where water freezes and boils: a circle for freezing and a square for boiling. Label the axes and give the graph an appropriate title.

Problem 4: Use Matlab's anonymous function facility to define a farenheit2celsius function at the Matlab prompt, instead of writing it in a file as in problem 1.

Problem 5: Use matlab's fsolve function or your newtonsearch function and the farenheit2celsius function from problem 4 to find the temperature that has the same numerical value in F and C. Verify your answer by solving the equation with algebra.

Problem 6: Verify your answer from problem 5 by evaluating your farenheit2celsius function at the value found as an answer to problem 5.

Problem 7: Write a script that produces a multiplication table like this

 1  2  3  4
 2  4  6  8
 3  6  9 12

only for the numbers 1 through 10 in both the rows and columns. Using two nested for-loops and the fprintf function with a formatting code like in problem 2 to get uniform spacing.

Problem 8: Find a solution to the system of equations

using Matlab's fsolve function or your newtonsearch.

Problem 9: Deduce the functional relationship y(x) for the data in this plot.

Problem 10: Assume you have a file data.asc containing the data for the above graph, with the x values in the first column and the y values in the second column. Write the Matlab code that would load the data and produce the above plot.