2009 - Fall

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: Wednesday, September 16, 2009 at class time

Problem 3.4 on page 72 gives you an infinite series that converges to π4/90. Compute the sum of this series using only the first term and calculate the true error, Et. (Use your calculator to obtain a "true" value of π4/90.) Repeat this computation using the first two, then three, then four terms of the series, computing the errors each time. Is the estimate getting better?

Problem 5.3 part b on page 131

Problem 5.3 part c on page 131.

Problem 6.1 on page 157, but only do 3 iterations.

Use Newton's method on the function in problem 6.1 and iterate 3 times. Start with an initial value of x0 = 1. How does this method compare to your results using fixed-point??

Assignment 2

Due: Monday, October 12, 2009 at class time

Problem 6.14 on page 158

Find the inverse of

using LU-decomposition.

Problem 9.10 parts c and d. For Gaussian, be sure to show the steps very clearly, noting the multiplying factors you use at each step. I reallly don't need to read what your calculator tells you.

Problem 11.3 on page 303. This problem requires you to use a method/algorithm I did NOT go over in class, but it's very important that you realize its importance. Be careful with the book's write-up; the algorithm can be a little confusing.

Problem 11.11 part a. Do 3 iterations and compute the ea's.

Assignment 3

Due: Wednesday, Oct. 28, 2009 at class time

Problem 17.10 on page 472. Disregard the instructions to plot.

Problem 17.16 on page 473. Disregard the instructions concerning standard error and correlation coefficient.

Problem 18.5 on page 506.

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

Assignment 4

Due: Wednesday, Dec. 2, 2009 at class time

Problem 22.2 on page 631.

Problem 24.17 on page 660

Use Euler's and Huens methods on the following IVP with the step sizes of 0.2 using 2 iterations, and then 0.1 using 4 iterations. Compare your answers at 0.4 with the true values computed with the solution provided.