2004 - Summer

General Homework

page 21: 1.1 - 1.7, 1.9, 1.10

page 72: 3.4, 3.6, 3.7, 3.8

page 97: 4.1 - 4.8, 4.14, 4.16

page 131: 5.1 - 5.3, 5.5, 5.7, 5.8

page 157: 6.1 - 6.7, 6.10, 6.11

page 203: 8.2, 8.3, 8.18

page 261: 9.1 - 9.3, 9.5 - 9.11

page 283: 10.3 - 10.5

page 303: 11.1, 11.2, 11.6, 11.8

page 472: 17.5, 17.6, 17.8, 17.9, 17.15

For interpolating polynomial, make up your own data and compute the polynomials(both Newton's and Lagrange). Also, consider the following problems:

page 558: 20.22, 20.23, 20.26, 20.31

page 610: 21.1a,c, 21.2a,c, 21.3a,c, 21.4a,c, 21.5a,c, 21.11a-d

Assignment 1

Due: Fri. June 18, 2004 at class time

Problem 4.2 on page 97 except do this for a Maclaurin series you derive (as I did in class) for tan-1x. Estimate the value of tan-1(1).

Problem 4.7 on page 97.

Problem 5.7 on page 131.

Problem 6.1 on page 158 but use BOTH fixed-pt and Newton's methods.

Assignment 2

Due: Friday, July 2, 2004 at class time

Problem 9.10 on page 262.

Calculate the LU decomposition of the matrix in the preceding problem and use it to find its inverse.

Problem 10.19 on page 284.

For problem 11.11a on page 303, apply Guass-Seidel method 3 iterations and calculate the ea's

Assignment 3

Due: Monday, July 12, 2004 at class time

Part a) Problem 17.7 on page 472

Part b) Problem 17.8 on page 472

Part c) Compare the results of parts (a) and (b) above. Conclusions?

Problem 17.22 on page 473.

Problem 20.33 on page 559.

Find the natural spline that passes through the points {(xk , f(xk))} 3k=0, on the graph of f(x) = x + 2/x, using the nodes x0=1/2, x1=1, x2=3/2, x3=2. Check the accuracy of your interpolant at the value x = 3/4. Check it again at the value x = 7/4.

Assignment 4

Due: July 26, 2004 at class time

Problem 21.11 a - c, page 611.

Problem 22.2, page 631.

Use Euler's and Huens methods on the following IVP with the step sizes of 0.2 and then 0.1 (2 iterations and then 4 iterations). Compare your answers with the true values computed with the solutions provided.

Solve the same problem as in #3 above, but using the classical RK-4 method. Compare the value obtained from this method at t = .2 with those obtained in #3 above.

Assignment 5

For this assignment, you will submit C++ compilable files containing a program written in C++. To submit files to the gradebook electronically, from the directory inwhich the files reside, type in at the UNIX prompt the command: csubmit <filename1> <filename2> etc. Name your files meaningful names and give them appropriate extensions. Also, make sure that you compile and run your program using the GNU (g++) compiler before submitting to make sure that it will work in the gradebook. The compiler command (from the UNIX prompt) is:

g++ -Wall -W -s -pedantic-errors myfiles.cpp -o executable_name

Concept: As you should remember, we studied the various methods of solving sets of linear equations using Gaussian elimination and pivoting techniques. Some pivoting techniques work poorly (so poorly that they won't work!) and some do better. You are to compare these techniques in this assignment. Specifications: Your code is to read in from a file the size of the system to solve and then the rows of the coefficient matrix followed by the "b" vector on the right-hand side of the system. Your program can store the information in any manner you wish, be it dynamically allocated memory or static memory. Your program is to solve the system using three pivoting techniques: naive pivoting (none at all), partial pivoting, and scaled partial pivoting.

Test your code on your own test problem to see how the answers compare. Make your test problem so that naive will fail - see what happens! Make your test problem ill-conditioned too to see how the two other methods work.

Details: In order for you to submit this to the gradebook, you will need to run a short script in your AFS UNIX account. It is:

~cpp/bin/53setup

Log off after that and then log on again. You should have what you need then. I also have to set up drop boxes for you before you can submit, so don't submit any files until I tell you that everything is set up.

If you have any questions, be sure to ask me.