Helpful Matlab functions

sum, any, all, linspace
plot, semilogy, semilogx, xlabel, ylabel, legend, axis, 
hist, randn

Problem 1: Write a Matlab expression that sums the first N of each series and evaluate it for N=100.

(a) 1 + 1/2 + 1/3 + 1/4 + …
(b) 1 + 1/2 + 1/4 + 1/8 + …
(c) 1 + 1/3 + 1/9 + 1/27 + …
(d) 1/2 + 2/3 + 3/4 + 4/5 + …
(e) 1/2 - 2/3 + 3/4 - 4/5 + …

Problems 2,3 and 4: Test that your expression gives the right answer on a good set of test vectors. But please turn in just the general Matlab expression, not the tests.

Problem 2: Given vectors x,y of the same length, write expression that has value true (1) if each component of x is greater than the corresponding component of y, false otherwise.

Problem 3: Given vectors x,y of the same length, write expression that has value true (1) if any component of x is greater than the corresponding component of y, false otherwise.

Problem 4: Given vector x, write expression that has value true (1) if the elements of x are sorted in increasing order (that is, if no element is less than the previous element) and false otherwise.

Problems 5-11: Turn in the Matlab code and the figures. Always label the figures appropriately, using title, xlabel and either ylabel or legend. The figures should be titled “Problem 5”, etc. Read help for the following functions and then experiment with them to see how they affect the plot.

figure, clf, hold on, hold off
grid, xticks, yticks 
axis([xmin xmax ymin ymax), axis equal, axis square

Problem 5: Plot sin(x) versus x for 100 evenly space points in x from 0 to 2pi, using a solid blue line.

Problem 6: Plot sin(x) in red, cos(x) in green, over same x as problem 5. Use 'legend' to indicate which function is shown in which color.

Problem 7: Plot for 40 evenly space points in x from -2 to 2, using a red line and a circle on each data point. Superimpose an x,y grid on the plot.

Problem 8: Make a plot of the unit circle. Make sure it's closed –no gap! Hint: use linspace to specify a range of angles, then cos and sin to produce vectors of the x,y coordinates of points on the unit circle.

Problem 9: Plot for 100 points x evenly space between -2 and 5. Choose the most appropriate plotting function. Hint: it ain't plot!

Problem 10: Plot for 100 points x evenly space between 1 and 4. Choose the most appropriate plotting function. Again, it ain't plot!

Problem 11: Make a histogram of 1000 random numbers from a normal (Gaussian) distribution. Use Matlab's hist and randn functions.