SNC_2015
Symbolic and Numeric Calculations
ISC 3222 - Fall 2015

SNC_2015 contains some information used when I taught an the introduction to MATLAB section of Professor Ming Ye's class ISC 3222, "Symbolic and Numeric Calculations", 30 September 2015.

I gave the students a summary sheet in matlab.txt.

During the class, I posed the following questions to the students, and we discussed approaches to solving the problems, and I demonstrated several versions of MATLAB programs to solve them.

• AREA: The integral of f(x) from x1 to x2 is the area between the x axis and the curve. If we can't use calculus, what other methods can compute or estimate this area?
• CLOCK: At 2:00, the minute hand (pointing at 12) is "behind" the hour (which points to 2). At 3:00, the minute hand has passed the hour hand. When did the two hands meet?
• CURVE: How long does it take to make a plot of 5000 values of y = cos ( 100 * x ) - 4 * erf ( 30 * x - 10 )?
• HAIL: Start with a number N. If it's even, divide it by 2. If it's odd, multiply by 3 and add 1. Repeat. Eventually, you reach a value of 1. Count how many steps it took. This is the hailstone number of N. Do we see a pattern if we compute and plot HAIL(N) for many values of N?
• NEAREST: Given a table of city locations, how could you find the nearest city to each city?
• POWERS: Make a table of powers 2^n? How far can we go before we see the effects of computer arithmetic? What about a table of (2^n)-1?
• TANK: A spherical water tank has radius R. If it is filled to a depth H, what is the volume V of water it contains? If we can weigh the tank and determine the volume V, then what is the height of the water in the tank?

AREA:

• area1.m, estimates area between X axis and Y=3/4*(1-X^2).
• area2.m, estimates area between X axis and Y=3/4*(1-X^2); this version has comments.
• area3.m, estimates the area of a hand, as outlined in data points in a file.

CLOCK:

• clock1.m, plots the minute and hour hand positions between 2 and 3 o'clock.
• clock2.m, plots a function that is the difference between minute and hour hand rotations.
• clock3.m, tries to solve the clock problem by repeatedly splitting the interval.

CURVE:

• curve1.m, makes a plot one dot at a time.
• curve2.m, makes the same plot, using vectors.

HAIL:

• hail1.m, computes 10,000 hailstone numbers and plots them.
• hail2.m, computes all the hailstone numbers at the same time.
• hail3.m, does a single check for even/not1 and odd/not1 numbers.
• hail4.m, does a double find, which requires indexing the index.

NEAREST:

• nearest1.m, seeks the nearest neighbor to 100 random cities.

POWERS:

• powers1.m, prints powers of 2 up to 2^N.
• powers2.m, compares 2^N and 2^N-1
• powers3.m, represents integers by a vector of M binary digits.

TANK:

• tank1.m, plots the volume as a function of height for the tank problem.
• tank2.m, makes the tank plot using a MATLAB function.
• tank3.m, makes the tank plot using a vector function.
• tank4.m, seeks the height H which corresponds to a given volume V.