channelflow.org

Site Tools

gibson:teaching:fall-2014:math445:hw2

Math 445 HW 2: array operations and basic plotting

```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.