Honors MP - Answers
Name: _________________________________ NetID:
_____________________ Section#: ______
Part 1: Monte Carlo
1. Write the Matlab command using 'vol' to compute the volume of the
ellipse using 1000 points.
_________________________________________________________________
2. What is the result from above?
_________________________________________________________________
3. Rerun the command in (1) with 10,000 and then 100,000 points
and write down the results.
___________________________
___________________________
4.Compare these results with the actual volume. When we increase
the number of points does the accuracy improve in general?
Explain your answer. (Hint: research the expression "The Law of
Large Numbers" (look this up in Wikipedia))
_________________________________________________________________________________________________________
Part 2: adaptive integration
1. Write down the two
missing lines of code.
area =
___________________________________________________________ ;
area =
_____________________________________________________________________________________________________
;
2. Write the value of the
calculation:
area =
______________________________________________________________________________
Part 3: Harmonic Oscillator
1. Based on the ODE equation stated in the instructions write the
ODE as a system of two equations:
Don't write Matlab code, just write the math form
of the equations.
dx/dt =
____________________________________________________________________
dv/dt =
____________________________________________________________________
2. Now run your code by typing in the following ( after you have
filled in the blanks). See step 3 Refine, Generalize, ... to get the
values.
>> [t , xv ] = ode45(
@xvprime , _________________________,
____________________________ )
3. Fill in the blank to plot x versus time.
>> plot( t ,
_________________________________ )
4. Fill in this blank ____________________ to indicate which
of the cases
a. m = 1, k =
100, b = 2
b. m =
1, k = 100, b = 20
c. m =
1, k = 100, b = 5
matches the plot below.
Part 4: Ray Tracing
1. Light rays coming in from a star are effectively parallel and
should be focused to a single point. Notice that only one of the
mirrors does this. Which one of the mirrors reflects the star light
to a point? (Circle / Ellipse / Parabola)
____________________________________________________________________
Your solution to this MP should include the answering the questions
on this Answer webpage ( answer_sheet
)and emailing the answers and all of the following files to
(Jiahui Jiang ta8cs101@cs.illinois.edu).
inEllipse.m
adaptive.m
xvprime.m
ray_trace.m
and the three plots you generated from part four,
circle.jpg
ellipse.jpg
parabola.jpg