2005 - 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 17, 2005 at class time

Problem 4.3 on page 97.

Problem 4.5 on page 97.

Problem 5.6 on page 131.

Problem 6.6 on page 158.

Assignment 2

Due: Wednesday, July 6, 2005 at class time

Problem 9.8 on page 262 but use scaled partial pivoting

Calculate the LU decomposition of the matrix below and use it to find its inverse.

Problem 17.6 on page 472.

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

Assignment 3

Due: Tuesday, July 12, 2005 at class time

1. 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?

2. Problem 18.5 on page 506.

3. Problem 20.31 on page 559.

4. Find the natural spline that passes through the points {(x_k , f(x_k))} ³_k=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, 2005 at class time

1. Problem 21.12 a - e, page 611.

2. Problem 22.3, page 631.

3. 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 solution provided.