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====== Math 445 lab 2: plotting and scripts====== ==== Part 1: vector manipulation ==== Do the following in Matlab, saving your work to a file with the ''diary'' command, and labeling each problem with a Matlab comment (e.g. ''% problem 1''). 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. 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. What is the sum of every third number between 3 and 27, inclusive? 10. What is the sum of the integers between 1 and 100, inclusive? 11. Make x a vector from 0 to $2\pi$ in increments of 0.02. ==== Part 2: sums ==== ==== Part 3: plots ==== 12. Make a plot of the polynomial $f(x) = x^3 -5x^2 + 2x + 3$ as a blue line. In the same plot, draw a line along the $x$ axis. (Hint: in Matlab create a zero vector of the same length as your $x$ vector with ''y=0*x'', then plot $y$ versus $x$ along with $f$ versus $x$.) Using this plot, estimate the zeros of the polynomial, i.e. the values of $x$ for which $f(x) = 0$. Make sure to find all the zeros of $f$ by adjusting limits of the plot until all intersectionf of $f$ with the $x$-axis are visible. 13. Make a plot of a unit circle, i.e. a curve that satisfies $x^2 + y^2 = 1$. 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 $x^2 + y^2 = 1$. Instead parameterize the curve in terms of the angle $\theta$, i.e. calculate $x$ and $y$ from $\theta$.
