Embedded Files
General Homework
Chapter 1:
page 12: 1, 2, 8a, 9a, 11a,b, 12b,c 13, 14a
page 23: 1a, 2a, 3a,b, 4a, 6, 7, 8b, 13b,
page 37: 1a,b, 2, 3a, 5a,b,c, 6a, 12
page 50: 1b, 2, 3a,b, 4, 11
page 61: 3, 4, 5, 9, 10, 11
page 85: 1, 2, 3, 6 - 11, 13 - 15, 22
page 119: 1, 2, 4, 5, 8, 10, 13, 15
page 124: 1, 23, 4b, 7
page 137: 1, 2, 5, 9, 11, 14a, 15
page 153: 1, 3, 4, 6
page 165: 1, 8
page 181: 3, 5, 6
page 196: 1, 3 - 6, 8, 9
page 205: 1a,b,d,
page 217: 1a, b, c, 2a, 3a, 6
page 228: 1, 2, 5, 8
section 4.5: I will assign no explicit problems to do, though many of them are good problems. But I will expect you to know the principle idea behind the use of Chebyshev polynomials.
page 259: 1a, 2a, 3a, 4, 5, 8, 10a
page 275: 1, 3, 6a, some of 8 - 15, 17, 18, 19
page 295: 5, 9b
page 334: 1a,b, 2a, 3a
page 349: 1, 4
page 362: 1c, 2c, 3
page 374: 1a, 8b,c, 9b
page 389: at least 3 of the problems in #1
page 463: part a only for 1, 3, and 5
page 472: 1 - 6, 8, 9
page 480: 1 - 5
page 485: 5
page 502: 5
Assignment 1
Due: Thursday, Sept. 17, 2020 at class time
For these problems, calculate all results to 8 significant figures. Be sure to follow the RULES on homework submissions.
Problem 1:
i) page 23 #5a find the percent relative error
ii) Determine a base ten fractional expression (you know, like 3/65 or 88/153 or 5/9 or...) equal to 0.101101101101...
Problem 2: page 50 #2 parts a -> e
Problem 3: page 61 #6
Problem 4: page 85 #6 parts a -> c
Problem 5: page 86 #10
Assignment 2
Due: Thursday, Oct. 15, 2020 at class time
For these problems, calculate all results to 8 significant figures. Be sure to follow the RULES on homework submissions.
Problem 1: page 138 #13
Problem 2: page 153 #6
Problem 3: page 165 #6 Answer the question in the text, i.e. produce three iterates using both methods, but also solve the system using iteration, either Jacobi or Gauss-Seidel, iterating until you are reasonably close to the solution or until you guess the solutions after producing these iterates?
Problem 4: Apply fixed-pt iteration to f(x,y) = x2+xy-10 = 0 and g(x,y) = y+3xy2-57 = 0. First, rewrite the 1st equation by isolating the xy term and then dividing by y; rewrite the 2nd equation by isolating the y term. Iterate twice starting at (1.5, 3.5) to see what happens. Then, rewrite the first eqn by isolating the x2 term and taking the square root; rewrite the 2nd eqn by isolating the 3xy2 term, then dividing by 3x and taking the square root. Again start at (1.5, 3.5) and iterate twice...then guess the answer and check it.
Problem 5: page 182 #7
Assignment 3
Due: Thursday, Oct. 29, 2020 at class time
For these problems, calculate all results to 8 significant figures. Be sure to follow the RULES on homework submissions.
Problem 1: page 218 #2b
Problem 2: page 229 #7
Problem 3: page 261 #9a
Problem 4: page 276 #4
Problem 5: page 277 #17
Assignment 4
Due: ??????, 2020 at class time
For these problems, calculate all results to 8 significant figures. Be sure to follow the RULES on homework submissions.
Problem 1: page 349 #3
Problem 2: Compute approximations to ∫10 sin(√ X )dx using the Trapezoidal rule with h = 1 and then again with h = 1/2. Then use Simpson's 1/3 with h = 1/2 and h = 1/4. How do they compare?
Problem 3: Do the same computation as in #2 but using Boole's rule with h = 1/4. Which is the best approximation now?
Now, for the next two questions, let O.D.E. refer to y' = yt-2, y(1) = 2
Problem 4: For the O.D.E., using h = 0.5, compute an approximation to y(1.5) using Euler's method, then Heun's method, then the Midpoint method.
Problem 5: Now use RK-4 with h = 0.5 to generate an approximation to the solution to O.D.E. at t = 1.5 and t = 2.0. Now calculate the percent relative error to the exact solution given by y = 2e(t-1)/t at t = 2.0. Was it
good???! (ans: yes)
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