2002 - 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 21, 2002 at class time

1. Problem 4.3 on page 97.

2. Problem 4.5 on page 97.

3. Problem 5.5 on page 131.

4. Problem 6.6 on page 158.

Assignment 2

Due: Wednesday, July 3, 2002 at class time

1. Problem 9.8 on page 262.

2. Problem 10.4 on page 283.

3. Problem 11.8 on page 303 but do only 3 iterations.

4. Problem 10.17 on page 284.

Assignment 3

Due: xxxxxx 2002 at class time

1. a) Problem 17.7 on page 472

b) Problem 17.8 on page 472

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

2. Problem 17.22 on page 473.

3. Problem 20.33 on page 559.

4. 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, 2002 at class time

1. Problem 21.11a-c page 611.

2. Problem 23.4 page 643, but also use h3= /12

3. Solve the following problem: dy/dx = x2y - 1.2y, y(0) = 1

a) analytically (done for you in class if you were there)

b) graph the solution on the interval [0, 2]

c) generate estimates of the solution using Euler's method with h = .5 and h = .25

d) generate estimates of the solution using Heun's method with h = .5

e) generate estimates of the solution using Midpoint method with h = .5

f) compare the results of all these estimations at the point x = 1 using the true value of the solution at that point to compute true relative error values.

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