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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.
Problem 26.6 on page 751, but only for the first step (to 4.5). Thus, don't calculate the solution to 5.0.
Special Assignment
Due: Monday, May 11, 2009, by noon in IN MY OFFICE
Problem #26.6, page 751. Use Milne's (pg 747) with h = 0.5, find and estimate to y(5). Iterate the correctors 3 times and ignore the text's es's.
Problem #13.4 on page 353.
Problem #23.5 on page 644.
NOTE: This assignment will give you 5 pts per problem added to your total points. Do the "math" (arithmetic!) and determine whether it will make a difference in your grade before submitting.
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, February 4, 2009 at class time
Problem 3.5 on page 72 but use only 6 terms
Problem 4.3 on page 97.
Problem 4.7 on page 97.
Problem 5.9 on page 131.
Problem 6.10 parts a & b only on page 158.
Assignment 2
Due: Monday, March 2, 2009 at class time
Problem 6.14 on page 158. Use Newton's method for a system of non-linear equations and start with P0 = (1, 1). Do 2 iterations. The values in the Jacobian are going to be ugly. You can use your calculator for finding the inverse of that.
Problem 9.7 on page 262.
Calculate the LU decomposition of the matrix below and use it to find its inverse.
Problem 11.12 a on page 303.
Assignment 3
Due: Monday, March 9, 2009 at class time
Problem 17.9 on page 472.
Problem 17.18 on page 473.
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: Monday, April 27, 2009 at class time
Problem 22.1 on page 631.
Problem 24.16 on page 660
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.
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