gibson:teaching:fall-2014:math445:hw2

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.

gibson/teaching/fall-2014/math445/hw2.txt · Last modified: 2014/09/22 09:06 by gibson