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gibson:teaching:spring-2018:math445:lab2

# Math 445 lab 2: vectors, plots, and scripts

Do the problems for parts 1 and 2 at the Matlab prompt, saving your work to a file with the diary command.

Be kind to your teaching assistant!

• Label each problem with a Matlab comment (e.g. % ==== Problem 1 ====).
• For questions with free-form response, write your answer as a Matlab comment. Write in complete sentences!
• Reduce unnecessary whitespace with the format compact command.
• When you're done, edit the diary file to eliminate errors, so that your diary shows just the correct work.

### Part 1: Vector manipulation

Relevant Matlab

[] % square brackets
,  % row separator
;  % col separator
:  % colon operator
'  % apostrophe
linspace

1. Assign a row vector with elements 3, 4, 5, 9 to the variable u.

2. Assign the transpose of u to the variable w.

3. Change the third element of w to 10.

4. Assign a column vector with the elements 7, 1, -2, 3 to the variable z.

5. Add w and z. Does the result make sense?

6. Add u and z. Does the result make sense?

7. Create a vector of the even integers between 2 and 14, inclusive.

8. Create a vector of the odd integers between 7 and 19, inclusive.

9. Make x a vector from 0 to in increments of 0.02.

### Part 2: Computing sums

Relevant Matlab syntax

:        % colon operator
sum      % sum function
.* ./ .^ % dot syntax

10. What is the sum of every third number between 3 and 27, inclusive?

11. What is the sum of the integers between 1 and 100, inclusive?

12. The infinite series diverges as . Demonstrate this in Matlab by computing the sum for several values of , e.g. to by powers of ten.

13. The function can be calculated from the infinite series Of course we have to truncate this infinite sum to a finite number of terms in order to calculate it on a computer. How many terms do you need to keep in order to compute to sixteen digits accuracy? Hint: use format long to see all sixteen digits of the computation.

Are you amazed or what?

14. Now use the same infinite series for to calculate . How many terms do you need to keep in order get the correct answer to sixteen digits accuracy?

### Part 3: Plots

Relevant Matlab

.* ./ .^  % dot syntax
plot      % plot function
axis      % set limits on plot or aspect ratio
xlim      % set x limits
ylim      % set y limits
grid      % turn grid on/off
help      % help function

15. Make a plot of the polynomial as a blue line. In the same plot, draw a line along the axis. (Hint: in Matlab create a zero vector of the same length as your vector with y=0*x, then plot versus along with versus .) Using this plot, estimate the zeros of the polynomial, i.e. the values of for which . Make sure to find all the zeros of by adjusting limits of the plot until all intersection of with the -axis are visible.

16. Make a plot of a unit circle, i.e. a curve that satisfies . Draw the circle with a thick red line, label the axes, and give the plot a title. Make sure the circle looks like a circle and not an oval. Hint: don't try to draw the plot using the equation . Instead parameterize the curve in terms of the angle , i.e. calculate and from .

(I previously had a problem 17, revisiting the sum of …to be written. But on second thought, this problem belongs in lab 3. So expect it there.) 