Lab 2 covers Chapter 11 of Gilat, which is using the symbolic package of Matlab to find exact
solutions to mathematical problems. First, We should look at the Calculus I Overview linked on the
Matlab schedule, paying particular attention to "MATLAB Examples" on the last page (hopefully, 152
students already know the rest!)
g5cbp384x02 (syms,simplify,subs): Students create a symbolic variable (and expressions using this
variable) using the syms command (see Gilat pp350-353). To simplify a symbolic expression, there are
several commands, all outlined in pp354-357. To substitute a value in for x, use the subs command
(372-375)
g5cbp386x10 (solve, ezplot): Define x and y as symbolic variables, then define the equations of the
ellipses and use ezplot (pp369-371, along with hold on: pp142-143) to plot both ellipses on the same
graph. Use the solve command pp360-363) to find the points of intersection. NOTE that the easiest
syntax is [var1 var2] = solve(eq1, eq2, var1, var2) (see examples on p361) so the solutions will be
immediately displayed.
TIME TO MAKE IT RELEVANT TO CALCULUS!!! For the remaining 3 problems, students will
apply these symbolic techniques to area and volume problems from the Stewart textbook.
s427x18 (solve, ezplot, int): Students explain the steps needed to find area: 1) plot graphs, 2) find
intersections by solving, 3) set up and evaluate the integral (Top-Bottom OR Right-Left). Pay
attention to that tthe same process works in MATLAB-only MATLAB does the "grunge calculations"
for you! So the process is: 1) use ezplot (and hold on as above) to plot the graphs, 2) use solve to find
the intersections, 3) based on the graph, set up an integral (or more as needed) and evaluate using the
int command (pp365-366).
s438x28 (solve, ezplot, int): Same as above, but plot the region you would rotate You can use Maplet
#111 to help with the setup if necessary), solve to find the intersections, and set up the volume integral
and evaluate using the int command.
s444x26 (solve, ezplot, int): Same as above. The beauty of 'ezplot' is that it WILL easily graph these
functions (unlike their calculator!!!). Also remind in mind that, just like by hand, you will have to
adjust the radius since they are rotating around a different axis!
Let me know if you have any questions about any of the topics. In addition, Students should go over
Maplets 110-111 to prepare for recitation. BOTH Maplets are extremely helpful for students to
visualize the volume problems in 7.2 and 7.3 (#111 on rotations, #110 on "base is...cross sections are..."
problems)