MATH 303: Scientific Computing
Homework Assignments
- Assignment 1: Send me an e-mail (from you NOT default, Not some organization who will let you use their account . . .) to which I can reply - stating (Truthfully) that you have read and understand the syllabus & class policies.
- Assignment 2: Figure out how to read data from a file into Maple and plot the points found in the data file bifer.txt found in the henson/mathcosc/MATH303 subdirectory on the students' K:/drive on the campus network.
- Assignment 3: Copy the file llsdata.wb3 from the math303 subdirectory on the K:\drive to a floppy or your P:\ drive. There are four sets of x,y data in this worksheet.
- Export the data into (a) text file(s) and write a program that will find the best fit line y=ax+b in the sense of least squares to each set of data and which will calculate the coorelation coeficient for the data.
- Use a spreadsheet to find the least squares linear fit and the coorelation coeficient for each set of data. Create a plot of the data and of the line.
- Use Minitab to find the lines & the coorelation coeficients as above and to graph the data and the least squares line.
- Assignment 4: (Due 3/19 by 5 p.m.) Find the unit round using a spreadsheet and a program. are they the same? Why or why not? Try to complete the problems passed out in class - do not hand on your solutions but rather hand in a narrative about them. What to hand in:
- a narrative about the problems from the text that I handed out in class.
- the code for your program to find the unit round (with documentation)
- The unit rounds that you found with the program and the spreadsheet.
- a narrative with all the usual questions addressed plus: compare the two unit rounds and describe how you found the spreadsheet one.
- Assignment 5: (Due: April 5) Use the data collected in class to investigate the relationship between the period of oscillation of a pendulum and the length of its arm. Use appropriate tools (as discussed in class) to analyse your data.
- Assignment 6: Use either a spreadsheet or a computer program (or a combination of both) to approximate the solution to x' = 1/x2 - xt; x(1) = 1 on the interval [1,2] using both Euler's Method and the classical fourth order Runga Kutta Method with step sizes of h = 2-n for n = 2, 3, ...7. Compare the answers you get for the different methods and the different step sizes. In your narrative discuss this comparison. Plot x vs. t for the different approximations when n=2, 4 and 7. Create the following (You may use any packages or a program for this):
- A graph with the n=7 Euler solution and the n=7 Runga Kutta solution on the same graph.
- A graph with the n=4 Euler solution and the n=4 Runga Kutta solution on the same graph.
- A graph with the n=2 Euler solution and the n=2 Runga Kutta solution on the same graph.
- A graph with the Euler solutions for n = 2, 4, and 7 on the same graph.
- A graph with the Runga Kutta solutions for n = 2, 4, and 7 on the same graph.
- Assignment # 7 (Due Monday May 10) May be completed in groups of 2 or individually. In the case of a group assignment hand in ONE assignment with 2 narratives.
- Model a pendulum using the theory we have discussed. Use a spreadsheet OR a computer language solution or some combination of the two. Find the subsequent motion of a pendulum for initial amplitudes of 10, 20, 30, 45, 60, 75, 80, and 90 degrees. You may assume the initial velocity to be zero. What happens if the initial amplitude is greater than /2 radians?
- What happens if the initial velocity is not zero? Try several nonzero initial velocities in your model. Find the subsequent motion of the system. In particular, try initial velocities of , /2, /4, and /6 radians per second with several of the larger values given in step 1. What happens if the initial velocity is much greater than radians per second? Test your answer with several values that are much larger than radians per second. Make sure you properly graph the result.
- Suppose one drives this pendulum with a sinusoidally varying force {F(t) = Asin(wt)}? Determine what the subsequent motion of the system will be. Choose a reasonable size force and indicate in your narrative why you chose that size force.
- The output should be graphical with proper titles and labeled axis. In particular, for each simulation, you will plot vs t (displacement vs time) and velocity vs displacement ( vs ). The plot of velocity vs displacement is known as a phase-space plot.
- Assignment # 8 (May be completed in groups of 2 or individually. In the case of a group assignment hand in ONE assignment with 2 narratives.) Write a program or a spread sheet to find the solutions of sin(x^2) = sin^2(x) and of (4-3/x)^(1/3)=0 using both Newton's method and the
bisection method. Find as many roots as possible (or seven which ever is least) and discuss the behavior of
both methods. (last assignment for those who attend all four classes during the weeks of 4/19-4/30)
