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Math 2280-1
2280-1 home page
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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 14
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 solution formula. 34 = 2 points, 39 = 1 point.
Due January 21
1.3: 3, 6, 11, 12, 13, 18, 21, 23, 29; for 6 use dfield to draw the slope field (google it, or alternately use the Math Department computers and type dfield & after the prompt > in a terminal window and hit enter to get a version which will let you print without taking a screen shot. Call this 6a. Then do
6b verify that y(x)=x+C*exp(x) solves this DE, and
6c use dfield to sketch several solution trajectories onto the slope field and explain why these curves are consistent with your general solution formula.
29=29a; for 29b use dfield to illustrate several of the non-unique solutions that you verify exist in 29a.
1.4: 9, 12, 19, 22, 35, 41, 43, 46, 54, 66;
1.5: 1, 7, 13, 34, 36, 38, 41.
hwsols2.pdf
Grading: 28 points, distributed as follows:
1.3: 6b (verify solution part) = 1 point, 12, 13, 18 = 1 point each, 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, 38, 41 = 2 points each.
Due January 28
2.1: 1, 4, 5, 10, 13, 15, 24, 33;
2.2: 1, 7, 9, 12, 17, 21, 23.
Maple homework: maplehw1.pdf, maplehw1.mw version to open from Maple
mapleintro.pdf Maple and Math Dept. computer lab introduction
mapleintro.mw Maple version
maplecommands.pdf Useful commands for 2280
maplecommands.mw
hwsols3.pdf
maplehw1sols.pdf
Grading: 30 points, distributed as follows:
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 ); 23 = 2 points.
maplehw1 one point per problem, 1-8.
Due February 4
2.3 : 2, 3, 9, 11, 13, 14, 15, 16, 17, 18, 24, 25
2.4 : 5, 29, 29a by hand, 29bc probably in Maple or with other software.
2.5 : 5, 25 In 25 also compare numerical answers to exact answers obtained by solving this IVP by hand.
2.6 : 5, and famous numbers revisited, page 145.
numerical1.mw Maple notes from Monday January 25 - contain useful subroutines for 2.4-2.6 problems.
hwsols4.pdf section 2.3 and 2.4.25
numericalsolutions.pdf the rest of sections 2.4-2.6
Grading: 25 points, distributed as follows:
2.3: 2a = 2 points, 2b = 1 point, 9, 11, 13 = 2 points each; 17 = 3 points, 24 = 2 points.
2.4: 5 = 2 points, 29 = 3 points.
2.5: 5 = 2 points.
2.6: 5 = 2 points, famous number Pi = 2 points.
hwsols4.pdf
numericalsols.pdf
Due Monday February 7 - due date extended to Wednesday Feb. 9, 5:00 p.m.
Maple homework 2: maplehw2.pdf, maplehw2.mw version to open from Maple. This is a project you may do by yourself or with one other person.
Due February 11
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 now due next week.)
hwsols5.pdf
Grading: 26 points, distributed as follows:
3.1: 4, 11, 13 = 2 points each; 17, 34 = 1 point each.
3.2: 2, 9, 13, 22, 26 = 2 points each.
3.3: 10, 14, 29, 37 = 2 points each.
Due Wednesday February 16 due date extended to February 18
3.4 : 4, 5, 6, 13, 15, 19, 23.
3.5 : 3, 4, 17, 19, 36, 37, 43, 49, 50, 51, 64;
hwsols6.pdf
Grading: 24 points, distributed as follows:
3.4: 4 = 3 points, 5, 6, 15 = 2 points each;
3.5: 3, 17, 19 = 2 points each; 37 = 3 points, 43a, 43b, 49 = 2 points each.
Due February 25
3.6 : 4, 5, 7, 13, 16, 20, 21, 22;
3.7 : 2, 3, 4, 7. section 3.7 postponed until next week.
hwsols7.pdf
Grading: 10 points, distributed as follows:
3.6: 4, 5, 13, 20, 22 = 2 points each;
Due March 4
3.7 : 2, 3, 4, 7.
4.1 : 1, 8, 11, 15, 16, 21, 24, 26;
Class exercises I,II in feb28.pdf notes, last page.
hwsols8.pdf
Grading: 19 points, distributed as follows:
3.7 3 = 3 points, 7 = 2 points;
4.1: 8 = 1 point, 15 = 3 points (1 point for picture); 21ab = 1 point each; 24, 26 = 2 points each.
Class exercises I, II = 2 points each.
Due March 11
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 "numerical1" in the February 4 hw set above, 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; 5.3.16, 5.3.17 won't be graded until next week's homework assignment.
hwsols9.pdf
Grading: 32 points, distributed as follows: (long assignment!)
4.3: 9 = 4 points (2 points/part)
5.1: 13, 18 = 1 point each; 22, 26, 31 = 2 points each.
5.2: 3, 15, 27, 35 = 3 points each.
5.3: 3 = 2 points; 9, 14 = 3 points each.
Due March 18
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 11 class notes about the modeling, and March 9 class notes for the Maple commands. And here's a handout showing how to make cleaner-looking output for the eigendata: eigendata.pdf
5.3: 16, 17;
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.
hwsols10.pdf
Grading: 16 points, distributed as follows: (long assignment!)
5.3: 16 = 2 points, 17 = 3 points;
5.4: 1 = 3 points, 7 = 2 points; 11, 29 = 3 points each.
Due March 30 (Wednesday) (but you can use your hw to study for the exam, and hand it in on Friday instead).
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
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: 18 points, distributed as follows:
5.5: 3, 11, 23, 36 = 2 points each.
5.6: 13, 15 = 3 points each; 19, 23 = 2 points each.
Due April 8
Note: If you hand this homework in after noon on Friday this week, give it to Paula Tooman and the front desk of the Math Department office JWB 233, before 5:00 p.m. Do not slide hw under my office door after noon, as I will be away after then.
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 15 Note: If you hand this homework in after noon on Friday this week, give it to Paula Tooman and the front desk of the Math Department office JWB 233, before 5:00 p.m. Do not slide hw under my office door after noon, as I will be away after then.
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: 30 points, distributed as follows:
6.3: 8, 10 = points each; then 2 points for pplane picture and pointing out consistency between 8,10 and the nonlinear problem; 17, 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, 28 = 2 points.
7.2 4 = 2 points, 6 = 4 points.
Due April 22
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: 26 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; 20 = 3 points, 30 = 4 points;
9.2: 2, 9 = 3 points each.