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Differential Equations
2250-4 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.
Our course TA Victor Camacho has written up guidelines for how you should present your homework solutions,
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, 8, 11, 12, 13, 14, 21, 24; for 8, 24, use dfield (you can google the applet; alternately on the Math Department system after the prompt > in a terminal window type dfield & and hit enter, to run a version which lets you print without taking screen shots.
1.4: 3, 4, 9, 12, 14, 19, 20, 22, 40 45, 49, 54;
1.5: 1, 7, 8, 13, 20, 33, 36, 38, 41.
Maple Introduction: Read the .pdf's of the notes below. Open Maple, and use the "open URL" menu item to open the actual Maple worksheets (*.mw), and work through the examples they contain. Try to modify the example commands and see if you get what you expect. There is nothing to hand in from this portion of your assignment.
mapleintro.pdf
mapleintro.mw
maplecommands.pdf
maplecommands.mw
hwsols2.pdf
Grading: 30 points, distributed as follows:
1.3: 8, 12, 14, 24 = 2 points each;
1.4: 4, 9, 20, 40, 54 = 2 points each;
1.5: 8, 13, 20 = 2 points each, 36a = 1 point, 36b = 2 points, 41a = 1 point, 41b = 2 points.
Due January 28
2.1: 1, 3, 6, 8, 9, 12, 22, 33;
2.2: 5, 7, 9, 12, 14, 15, 23.
Maple homework: maplehw1.pdf, maplehw1.mw version to open from Maple
hwsols3.pdf
maplehw1sols.pdf
Grading: 26 points, distributed as follows:
2.1: 3, 8 = 3 points each; 12, 22 = 2 points each;
2.2: 7, 9, 14 = 2 points each, 23a, 23b = 1 points each.
maplehw1 one point per problem, 1-8.
Due February 4
2.3 : 2, 3, 9, 10, 12, 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
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.
Grading: 18 points, distributed as follows:
2.3: 2, 9 = 2 points each; 10, 12 = 3 points each;
2.4: 5 = 2 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 is extended to Wednesday February 9 at 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
Do the following book problems by hand, but please use software to check any computations you wish. In addition to the hand work which you hand in, also hand in technology (Maple, Matlab, etc.) checks for 3.3 20 and 3.4 13.
3.1: 1, 4, 11, 16, 17, 19, 23, 29, 32, 33, 34;
3.2: 7, 8, 9, 13, 17, 29, 30;
3.3: 13, 20, 33, 34;
3.4: 3, 5, 7, 10, 13, 19, 31, 32, 34, 39, 40, 44;
hwsols5.pdf
Grading: 20 points, distributed as follows:
3.1: 16, 19, 23 = 2 points each;
3.3: 13 = 1 point, 20 = 3 points (1 point for tech check), 34 = 1 point;
3.4: 5, 7 = 1 point each; 13 = 2 points (1 point for tech check), 19, 31ab, 40ab = 1 point each;
Due Wednesday, February 16 (due date extended until Friday Feb. 18)
3.5: 5, 7 , 8, 13, 22, 23, 30, 31, 32, 33;
3.5 technology checks (hand in printout): 22, find A-1, and verify that A(A-1)=(A-1)A=I; 23.
3.6: 2, 6, 17, 21, 22, 32. On 22 and 32 find x (just x1 in 32) with Cramer's rule. Then compute A-1 with adjoint formula (page 214), as well as with rref algorithm (better get same answer!) Finally, use A-1 to solve Ax=b, and compare first component with your Cramer's rule computation. The first exam, on Thursday February 17, will cover through section 3.6.
hwsols6.pdf
Grading: 18 points, distributed as follows:
3.5: 13, 22 = 2 points each; 30, 32 = 1 point each.
3.5: tech checks on 22, 23 = 1 point each. 3.6: 6, 17 = 2 points each; 22, 32 = 3 points each.
Due February 25
4.1: 1, 7, 9, 10, 15, 16, 19, 22, 25, 26,31,33;
4.2: 5, 6, 9, 15, 18, 24, 27, 29;
4.3: 1, 3, 6, 9, 10, 16, 17, 18, 23, 25. use technology to compute rref for any of these 4.1-4.3 problems, as long as you know you could do them by hand if necessary.
hwsols7.pdf
Grading: 21 points, distributed as follows:
4.1: 7 = 1 point, 10 = 2 points, 16 = 1 point; 19, 22 = 2 points each, 33 = 1 point;
4.2: 6 = 2 points, 9 = 1 point, 18 = 2 points;
4.3: 1, 3, 6 = 1 point each; 10, 16 = 2 points each.
Due March 4
4.4: 1, 2, 3, 6 8, 9. 11. 13. 26;
4.5: 1, 12, 16, 17, 26, 27, 28;
4.7: 1, 2, 3 4, 5, 6, 7, 8, 9, 10, 13, 15, 17, 21, 23, 25. feel free to use technology (Maple recommended, to help you practice) to compute rref for any of these 4.4, 4.5 or 4.7 problems, where appropriate.
hwsols8.pdf
Grading: 22 points, distributed as follows:
4.4: 2, 3 = 1 point each; 11, 26 = 2 points each.
4.5: 1, 12, 16 = 2 points each; 27, 28 = 1 point each.
4.7: 5, 7, 8, 13, 15, 17 = 1 point each; 25 = 2 points.
Due March 11
5.1: 2, 9, 11, 17, 27, 29, 30, 31, 34, 35, 39.
5.2: 2, 5, 9, 11, 13, 21, 22, 25, 26.
5.3: 3, 10, 14, 21, 22, 24, 29, 33, 37.
5.4: 4, 5, 7, 10, 12, 15, 17, 18, 23; In 15, 17, 18, use Maple (or other software) to create the requested graphs. Problem 5.4.23 is not due this week - it's been postponed
hwsols9.pdf
Grading: 28 points, distributed as follows:
5.1: 2, 11 = 2 points each; 27 = 1 point.
5.2: 2, 9, 22 = 2 points each, 26ab = 1 point each.
5.3: 10 = 1 point; 22 = 2 points, 33 = 2 points.
5.4: 4, 7 = 2 points each; 17, 18 = 3 points each.
Due March 18
5.4: 23.
5.5: 3, 4, 12, 13, 19, 34, 37, 43, 49, 50, 52.
5.6: 3, 5, 7, 14, 16, 21, 22.
EP 3.7: (supplemental electrical circuit section) 2, 3, 4, 7, 11, 20.
hwsols10.pdf
Grading: 27 points, distributed as follows:
5.5: 3, 12 = 2 points each; 34, 37 = 3 points each; 49 = 2 points.
5.6: 3, 7 = 3 points each; 22 = 2 points.
EP 3.7 2, 7 = 2 points each; 11 = 3 points.
Due March 30 (Wednesday) because exam 2 is Thursday ... and, as announced in class, you can hold on to this assignment until Friday.
10.1: 3, 7, 8, 13, 20 , 21, 23, 28;
10.2: 3, 4, 5, 6, 14, 19, 20, 28, 31;
10.3: 3, 7, 8, 17, 20, 27, 31;
hwsols11.pdf
Grading: 18 points, distributed as follows:
10.1: 8, 20, 23, 28 = 1 point each.
10.2: 4, 6, 20 = 2 points; 28 = 1 point.
10.3 8 = 1 point; 17, 20, 31 = 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.
10.4: 2, 3, 9, 10 , 15, 16, 29, 36;
10.5: 7, 13, 25, 31, 34;
6.1: 7, 17, 18, 24, 29;
6.2: 4, 10, 19, 28;
hwsols12.pdf
Grading: 24 points, distributed as follows:
10.4: 2, 10, 16 = points each.
10.5: 7 = 2 points, 34 = 3 points.
6.1: 7, 18, 29 = 2 points each.
6.2: 4, 10 = 2 points each, 19 = 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.
7.1: 1, 3, 5, 8, 11, 18, 21, 24, 26;
7.2: 5, 9, 10, 13, 14, 16, 21, 23, 25;
7.3: 3, 4, 6, 13, 14, 25, 30, 32, 37.
Use pplane (same URL as dfield - google it) for pictures. In 7.3.6 also solve with Laplace transform.
hwsols13.pdf
Grading: 27 points, distributed as follows:
7.1: 8, 18, 26 = 2 points each.
7.2: 9, 10 = 1 point each; 16, 21 = 3 points each; 25 = 2 points.
7.3: 4 = 3 points; 14, 30 = 4 points each.
Due April 22
7.4: 2, 3, 8, 13, 14, 16, 17, 18;
7.5 5, 6, 10, 11;
9.1: 5, 8, 11, 15, 20, 24;
9.2: 5, 6, 7, 8, 9, 14, 15, 19, 27, 30; use pplane to draw phase portraits as requested on hw problems.
hwsols14.pdf
Grading: Note: This was a long assignment. Our final assignment, for next week, will be much shorter. Also, I didn't look closely enough to realize that the text asked for so many phase portraits - I should have only had you actually print out several key examples. Sorry!
21 points, distributed as follows:
7.4: 8, 14, 17 = 3 points each.
7.5: none.
9.1: 11, 15, 20 = 2 points each (pplane picture not required on these if you sketched or described the output)
9.2: 6, 8 = 1 point each for the math and classification, no picture printout required; 19, 30 = 2 points for the math and classification. <
Due April 25 (Monday, 5:00 p.m.)
quakeproj.pdf browser-readable version
quakeproj.mw open this maple worksheet from Maple using "open URL" - modify it to make your solution file!
apr15.pdf contains commands which will help (after modification) with the earthquake project
Note: original version of April 15 Maple notes used the command "norm", which did not work for one of your classmates. The actual correct command in LinearAlgebra is "Norm", and I've changed the Maple file below to reflect this. Note: As on the earlier projects, you may work in teams of 2 people; make sure to put both your names onto the single project you hand in.
apr15.mw open from maple!
earthquakecomments.pdf explains why our forcing vector is the same on every floor, even though the building is being shaken at the bottom.
Due April 29
9.3: 8, 9, 10, 14, 15, 16, 17; In 8 and 10 use pplane to creat a phase portrait for the non-linear system (3) and explain how your linearizations compare to the phase portrait near the equilibrium solutions you're studying. Don't bother printing out any other phase portraits in this homework assignment, no matter what the text asks for.
9.4 9, 10, 11, 12, 14, 16.
Grading: this assignment is not being graded, but you are responsible for the material in these sections - make sure you understand these concepts and know how to do these sorts of problems.
hwsols15.pdf