This week, students will work on Lab 6 which covers chapter 5 of Gilat (using
element-by-element operations on vectors to produce plots) with a little twist:
they will fill in their enclosed regions! To start, read the material in the link
"Supplement 7" on the MATLAB schedule page.
g5c5p165x03: (plotting functions and labels): The method for plotting functions
is on pp139-140 of Gilat. Students will use element-by-element operations to
create a graph (*VERY IMPORTANT). Discuss the example on these pages in
detail, and especially note what happens if you choose a stepsize (delta-x) too
large (it would be especially interesting to show the plot with default size 1!). Let
them know that all graphs must include a title and axis labels (Gilat p144).
g5c5p166x14 (plotting functions, fill): Similar to the first example, but x and y are
both functions of t. Plot the parametrized curve in this problem and follow the
steps in Supplement 7, problem 3 to fill with the appropriate color (NOTE: there
are no points to plot in this one, so they don't use ALL the commands in the
example!)
g5c5p167x17 (plotting functions, fill): Plot the upper and lower halves of the
ellipse (NOTE: or they can parametrize the ellipse unless the directions say
otherwise-I do not have the book with me either and cannot seem to access it
online). Fill as done in Example 2 or 3 of the Supplement with the appropriate
color.
g5c5p170x29 (semilog, loglog): In this example, students will plot a function 3
times: Once using normal x and y axes (plot), once using a logarithmic scale on
the x axis (semilogx: pp149-150), and once using logarithmic scales on both
axes (loglog: pp149-150). Use the figure command to plot them in different
windows (details in the help documentation).
Problem 4 Supplement 7: students use symbolic differentiation to find the
equation of the normal line, use solve to find the intersections (see code for
Example 2 or Gilat ch 11 for review), fill to shade the area (and plot the corner
points with filled circles as done in the first two supplement problems), and int to
calculate the area. (NOTE: to fill, first plot x^2 from 0 to 2, then the normal line
from 2 to the intercept, THEN define x=[int:-0.1:0] and y=0*x: or define x as
usual and use the fliplr command mentioned in the Summary).