2006 - Spring

General Homework

chapter 1: 1, 5- 8

chapter 2: all

chapter 3: 1 - 3 +

chapter 4: 1 - 5, 7 - 10

chapter 5: 1 -3, 7, 8 +

chapter 6: 1 - 4, 6, 9, 11 +

chapter 7: 1 - 6, 8

chapter 8: 1 - 11

chapter 9: 1 - 5

chapter 10: 6, 9

chapter 11: 1 - 5, 7, 8

chapter 12: 1, 5 - 8, 10, 16

chapter 13: 1 - 3, 6

chapter 16: 2, 3, 5a,c

chapter 17: 1, 2a - c, 3, 4

chapter 18: 1b - d,2b - d, 5

chapter 19: 4

Assignment 1

Due: Fri. Jan. 27, 2006 at noon

problem 4.6, page 80. Also, include an explanation as to why no one in their right mind would use a truncated Taylor series to estimate a polynomial. What is the 6th order Taylor series for this polynomial?

problem 4.9, page 80.

problem 5.8 b, page 99.

problem 5.8 c, page 99.

problem 6.1, page 119.

Also, you will note that due time and date. You are welcome to bring your completed assignment to class on Thursday, if you wish to. If you turn it in any other time than class time, please bring them to my office and give them to me, my secretary, or put them in my mailbox in room 342 by the due time.

Assignment 2

Due: Thurs. Feb. 16, 2006 at class time

Solve using Newton's method for a system of non-linear equations:

0 = x² - 2x - y + 0.5

0 = x² + 4y² - 4

Start with (p₀,q₀) = (2.0, .25) and calculate two new points, (p₁,q₁) and (p₂,q₂). Show only the calculations for the first. You might want to employ Matlab for the calculations of the last point.

Problem 8.6 on page 158, but in part (a) replace "solve graphically" with "graph". You might want to appeal to how Cramer's method works in order to answer part (c). Give reasons.

For the system in problem 9.3, use LU-decomposition as I show you in class to find the LU-decomposition of the coefficient matrix.

Now use the LU-decomposition from the last question to solve the system in 9.3.

Find the inverse of

using LU-decomposition.

Problem 9.8 on page 171.

Also, you will note that due time and date. You are welcome to bring your completed assignment to class on Thursday, if you wish to. If you turn it in any other time than class time, please bring them to my office and give them to me, my secretary, or put them in my mailbox in room 342 by the due time.

Assignment 3

Due: March 7, 2006 at class time

Find the condition number for the Vandermonde matrix with x₁ = 4, x₂ = 2, and x₃ = 7. Normalize the rows before calculating the norms. Use the column-sum norm. Interpret your results.

Problem 12.7 on page 218.

Problem 13.8 on page 233.

Problem 14.10 on page 256 and calculate only the 5th order polynomial.

Find the natural spline that passes through the points {(x_k , f(x_k))} ³_k=0, on the graph of(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: April 20, 2006 at class time

Problem 16.5 on page 303

Problem 17.1 on page 319

Problem 17.4 on page 320

Problem 18.5 on page 344, but in part (b) use a step size of 50 yrs (so that you only do two iterations/applications of RK-4)

Problem 19.4 on page 363