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Math 2280-1
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Homework assignments will usually be posted a week before they are due (generally on Fridays). A subset of the underlined problems will be graded; if a problem is not underlined it is recommended but need not be handed in. Solutions and point values for graded problems will be posted after assignments are collected.
Due January 15
1.1 3, 6, 15, 16, 19, 27, 31, 34, 35, 36;
1.2 6, 7, 13, 18, 19, 20, 25, 29, 33, 34, 39.
hwsols1.pdf
Grading: 20 points, distributed as follows:
1.1: 6, 16, 19 = 2 points each; 31, 36 = 1 point each.
1.2: 6, 13, 18 = 2 points each; 20 = 3 points: 2 points for roughly accurate sketch, 1 point for correct values of x(5) and x(10). 34 = 2 points, 39 = 1 point.
Due January 22
see first page of jan15.pdf Note: postpone 1.5.34 and 1.5.38 until next week, since we only just started talking about these input-output models. But still do 1.5.41 which is a good exercise in modeling.
hwsols2.pdf
Grading: 27 points, distributed as follows:
1.3: 6b (verify solution part) = 1 point, 12, 13 = 1 point each, 18 = 2 points (1 point for showing uniqueness theorem does not apply, 1 point for finding two solutions to IVP), 29a= 2 points, 29b=1 point.
1.4: 9, 12, 22, 43, 54 = 2 points each; 66a = 1 point, 66b = 2 points.
1.5: 7, 13, 41 = 2 points each.
Due January 29
1.5 34, 38; warning: earlier I wrote 36 instead of 38, but I meant 38.
2.1 1, 4, 5, 10, 13, 15, 24;
2.2 7, 9, 12, 21, 23, 24;
hwsols3.pdf
Grading: 27 points, distributed as follows:
1.5: 34 = 2 points, 38abc = 1 point each.
2.1: 4, 5 = 3 points each (2 points solution formula, one point slope field picture); 10 = 2 points, 13ab = 1 point each; 15, 24 = 2 points each.
2.2: 7, 12 = 3 points each (equilibria, phase portrait and stability = 1 point, solution formula = 1 point, slope field or solution graphs = 1 point ); 24 = 2 points.
Due February 5 due date extended to Monday February 8, at 5:00 p.m.
project1.pdf browser readable
project1.mw open from Maple 12, edit and modify to do your first project.
Professor Gustafson's Maple page Lab 2, option 2, contains Maple hints which will help for this project.
project1notes.pdf for problems 1-3
amplitudephaseform.pdf how to go between a linear combination of sin and cos (with same angular frequency) and the amplitude-phase form.
Due February 5
2.3 : 2, 3, 9, 11, 13, 14, 15, 16, 17, 18.
2.4 : 5, 29 (29a by hand, 29bc probably in Maple.)
2.5 : 5, 25 In 25 also compare numerical answers to exact answers obtained by solving this IVP by hand.
2.6 : 5
hwsols4.pdf section 2.3
numericalsolutions.pdf sections 2.4-2.6
Grading: 22 points, distributed as follows:
2.3: 2a = 2 points, 2b = 1 point, 9, 11, 13 = 2 points each; 17 = 3 points.
2.4: 5 = 2 points, 29 = 3 points.
2.5: 5 = 2 points, 25 = 3 points.
Due February 12
3.1 : 2, 4, 5, 11, 13, 17, 27, 29, 30, 31, 33, 34, 35.
3.2 : 2, 5, 9, 11, 13, 21, 22, 25, 26.
3.3 : 3, 10, 14, 21, 22, 29, 33, 37.
(section 3.4 hw is due next week.)
hwsols5.pdf
Grading: 30 points, distributed as follows:
3.1: 2, 4, 11 = 2 points each; 17, 34, 45 = 1 point each.
3.2: 2, 9, 13, 22, 26 = 2 points each.
3.3: 10, 14 = 2 points each; 22 = 3 points, 29 = 2 points, 37 = 2 points.
Due February 19
3.4 : 4, 5, 6, 13, 15, 19, 23.
hwsols6.pdf
Grading: 15 points, distributed as follows:
3.4: 4 = 3 points, 5, 6, 15 = 2 points each; 19 = 3 points, 23a = 1 point, 23b = 2 points.
Due February 26
3.5 : 3, 4, 17, 19, 36, 37, 43, 49, 50, 51, 64;
3.6 : 4, 5, 7, 13, 16, 20, 21, 22. postpone 7, 13, 16, 20, 21, 22 until next week.
hwsols7.pdf
Grading: 21 points, distributed as follows:
3.5: 3, 17, 19 = 2 points each; 37 = 3 points, 43a, 43b, 49, 64 = 2 points each.
3.6: 4, 5 = 2 points each.
Due March 5
3.6 : 7, 13, 16, 20, 21, 22;
3.7 : 2, 3, 4, 7;
4.1 : 1, 8, 11, 15, 16, 21, 24, 26;
Class exercises A,B in mar1.pdf notes
hwsols8.pdf
Grading: 25 points, distributed as follows: (I originally told the grader to also grade 3.6 #4,5, but you did those last week. So I think he gave everyone 4 points for free, so that your totals are actually out of 29.
3.6: 13, 21, 22 = 2 points each;
3.7 3 = 3 points, 7 = 2 points;
4.1: 8, 16 = 2 points each; 21ab = 1 point each; 24, 26 = 2 points each.
class problem = 4 points (2 points for each part).
Due March 12
4.3 : 9; you may work with up to one other person on this problem, which requires you to write some Runge-Kutta code for systems. (You could start with the single differential equation version from an old Maple handout from Chapter 2, linked from our lecture page, and try to vectorize it).
5.1 : 11, 13, 18, 21, 22, 26, 31, 35;
5.2 : 2, 3, 9, 15, 27, 35; you may use Maple or other software to find eigenvalues/eigenvectors. Here are some clues to make your computations look better if you're using the LinearAlgebra package: eigendata.pdf
To plot the phase portraits you may use Maple or pplane...you can google an applet version (but the print command uses obsolete java so you'll probably need to print a screenshot), or use the Math Department version, which opens from a terminal window with the command "pplane &", and which has a functioning print command.
5.3 : 3, 7, 9, 14, 16, 17, 21;
hwsols9.pdf
Grading: 40 points, distributed as follows: (long assignment!)
4.3: 9 = 4 points (2 points/part)
5.1: 13, 18 = 1 point each; 22, 26, 31, 35 = 2 points each.
5.2: 3, 15, 27, 35 = 3 points each.
5.3: 3 = 2 points; 9, 14, 16, 17 = 3 points each.
Due March 19 Although I strongly encourage you to finish all of this assignment by Friday afternoon, March 19, so that you can enjoy your spring break, the class has convinced me to extend the due date until the Monday after break, March 29.
5.3 : Do the Maple exploration for section 5.3, pages 330-332. You may hand in joint work with one other person if you wish. Understand the set-up by carefully reading pages 330-331; we also discussed these issues in class, see the March 10 class notes for the Maple commands you will need and some comments on the modelng for this problem. Correction to March 10 notes: in LinearAlgebra you want to use "Norm", not "norm" (which is the linalg version.) I also handed out, but forgot to post, a handout showing how to make cleaner-looking decimal output for eigendata. Here is that handout: eigendata.pdf
5.4 : 1, 7, 11, 29; Work 1, 7, 11 by hand, except use the computer to draw the phase portrait for #1. You may work 29 by hand, but I'd recommend Maple to help you find chains.
5.5 : 1, 3, 11, 23, 36. Work by hand, except use Maple for eigenvectors. Also have Maple check exp(At), and hand in the Maple check. Here's how: MatrixExponential.pdf
hwsols10.pdf
Grading: 5.3 earthquake project will be graded separately. Section 5.4-5.5 hw is worth 23 points, distributed as follows:
5.4: 1, 7, 11, 29 = 2 points each.
5.5: 1, 3, 11, 23, 33 = 3 points each.
Due March 31 (Wednesday)
5.6 : 1, 13, 15, 19, 23. Do 13, 15 by hand. On 19, 23 you may use technology to compute variation of parameters formulas for the solutions, as long as you hand in printouts to verify your work.
hwsols11.pdf
Grading: 12 points, distributed as follows:
5.6: 13, 15, 19, 23 = 3 points each.
Due April 9
6.1 5, 8, 11, 15, 20, 24; use pplane to visualize your work in this section, as the directions indicate. However, you don't need to hand in any pplane hardcopies from this section.
6.2 5, 6, 7, 8, 9, 14, 15, 19, 27, 30. On 19, 27, use pplane to find and classify the other equilibrium solutions besides the origin, and print out and hand in the phase portrait justification (with sample solution trajectories). (For fun, you may wish to linearize about these other equilibria, to see how your pplane picture near the equilibrum corresponds to the solutions to the linearized system of DEs.)
hwsols12.pdf
Grading: 19 points, distributed as follows:
6.1: 5, 8, 11 = 1 point each; 15, 20 = 2 points each; 24 = 1 point.
6.2: 6, 8, 9 = 1 point each; 19 = 2 points, 27 = 3 points (pplane analysis is part of 19, 27), 30 = 3 points.
Due April 16
6.3 8, 9, 10, 14, 15, 16, 17; in 6.3.8 and 6.3.10 create a pplane phase portrait for the nonlinear system (3), and explain how your linearization computations are reflected in the non-linear behavior near the corresponding equilibria.
6.4 12, 13, 14, 15, 16.
7.1 3, 7, 8, 13, 20, 21, 23, 28.
7.2 3, 4, 5, 6, 14, 19, 20, 28, 31.
hwsols13.pdf
Grading: 37 points, distributed as follows:
6.3: 8, 10 = 2 points each, then 2 points for pplane picture and pointing out consistency between 8, 10 and the nonlinear problem ; 14, 16, 17 = 2 points each.
6.4: 12, 14 = 3 points each (2 points for linearization, 1 point for understanding nonlinear equilibria in these difficult borderline cases.)
7.1: 3 = 1 point, 8 = 2 points, 13 = 1 point, 20 = 2 points, 23 = 1 point, 28 = 2 points;
7.2: 4 = 2 points, 6, 14 = 4 points each;
Due April 23
7.3 3, 7, 8. 17. 20, 31;
7.4 2, 3, 36;
9.1 6, 7, 10, 13, 15, 17, 20, 30.
9.2 2, 9.
hwsols14.pdf
Grading: 28 points, distributed as follows:
7.3: 3, 8 = 1 point each; 17, 20 = 2 points each, 31 = 3 points;
9.1: 6, 7, 10 = 1 point each; 12, 20 = 3 points each, 30 = 4 points;
9.2: 1, 9 = 3 points.
Due April 30
9.3 1, 9, 17, 20;
9.4 1, 7, 9, 13;
9.5 1, 2, 7.
9.6 1, 5.
hwsols15.pdf
Grading: 26 points, distributed as follows:
9.3: 1, 9, 17, 20 = 2 points each;
9.4: 1, 7, 9, 13 = 2 points each;
9.5: 1, 2, 7 = 2 points each
9.6: 1, 5 = 2 points each