Math 2280-1
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Professor Korevaar
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Homework is generally due each Friday at the start of class, and solutions should be posted by the following Monday. The most recent assignments are listed first. Underlined problems are to be handed in, the remaining ones are optional.
Due Wednesday, April 26: Last assignment; Hurray!
9.5 1, 7, 13, 15, 16;
9.6 1, 4, 5, 11, 17, 21.
solutions15.pdf
Grading: 26 points, distributed as follows:
9.5: 1, 7 = 2 points each; 13abc = 2 points each; 15 = 3 points.
9.6: 1, 4, 5 = 2 points each; 11 = 3 points; 21ab = 2 points each (21cd not graded).
Due Friday, April 21:
9.1 3, 6, 7, 10, 12, 13, 15, 17, 20, 27, 28, 29, 30;
9.2 2, 9;
9.3 1, 9, 17, 19, 20;
9.4 1, 7, 9, 13.
solutions14.pdf
Grading: 34 points, distributed as follows:
9.1: 6, 10 = 1 point each; 12, 20 = 3 points each; 28 = 2 points;
9.2: 9 = 3 points;
9.3: 1, 9 = 3 points each; 17 = 2 points; 19, 20 = 3 points each;
9.4: 1 = 2 points (no graph necessary); 7, 9 = 1 point each; 13 = 3 points.
Due Friday, April 14:
7.2 19, 20, 28, 31;
7.3 3, 7, 8, 17, 20, 31;
7.4 2, 3, 9, 10, 15, 16, 29, 36;
7.5 11, 31;
solutions13.pdf
Grading: 23 points, distributed as follows:
7.2: 20, 28 = 2 points each;
7.3: 3, 8 = 1 point each; 17, 20 = 2 points each, 31 = 3 points.
7.4: 2, 10, 36 = 2 points each;
7.5: 11 = 1 point, 31 = 3 points.
7.1 3, 7, 8, 13, 20, 21, 23, 28.
7.2 3, 4, 5, 6, 14.
solutions12.pdf
Grading: 19 points, distributed as follows:
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 Friday, March 31: We restricted the problems on which you need to create "pplane" pictures: In 6.2 #19,27 use pplane to find and classify the other equilibrium solutions besides the origin, and print out a phase portrait for each problem. In 6.3 #8,10 create a phase portrait for the nonlinear system (3) and explain how your linearization compuations are reflected in the nonlinear behavior near the corresponding equilibria.
6.1 5, 8, 11, 15, 20, 24
6.2 5, 6, 7, 8, 9, 14, 15, 19, 27, 30
6.3 8, 9, 10, 14, 15, 16, 17
6.4 12, 13, 14, 15, 16.
solutions11.pdf
Grading: 35 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.
6.3: 8, 10 = 2 points each, then 2 points for pplane picture and pointing out consistency between 8,10 and nonlinear problem; 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).
Due Friday, March 24: except where indicated, work problems by hand, but feel encouraged to use technology to check.
5.4 1, 7, 11, 29
5.5 1, 3, 11, 23, 33, 36
5.6 1, 13, 15, 19, 23 On 19 and 23 you may use technology to compute variation of parameters formulas for the solutions. For more specific problem by problem instructions, see mar20.pdf lecture notes
solutions10.pdf
Grading: 34 points, distributed as follows:
5.4: 1, 11, 29 = 3 points each;
5.5: 1 = 2 points, 3 = 3 points, 11 = 2 points, 33 = 4 points, 36 = 2 points.
5.6: 13, 15a, 19, 23 = 3 points each;
Due Friday, March 10: (accepted until March 17) Because of the Maple project, the entire assignment for this week may be done in groups of up to three people...hand in one assignment per group.
5.2 2, 3, 9, 15, 27, 35 (You may use technology for eigenvectors, as long as you're sure you could find them by hand.)
5.3 3, 7, 9, 14, 16, 17, 21 (interesting!)
5.3 Maple exploration. See the paragraph near the bottom of page 327 which begins, "For your..." Here is a document we will discuss on Monday which contains useful commands, as well as another document which is a template you should use to carry out the project details:
mar6maple.pdf quaketemplate.pdf
mar6maple.mws quaketemplate.mws
solutions9.pdf
quakesols.pdf
Grading: 39 points, distributed as follows:
5.2: 3, 15, 27 = 3 points each.
5.3: 3 = 2 points, 9 = 4 points, 14, 16 = 2 points each, 17 = 4 points.
project: 2 = 2 points, 3, 4, 5, 6 = 3 points each; 7 = 2 points.
Due Friday, March 3:
4.1 1, 8, 11, 15, 16, 21a, 24, 26.
4.3 9 You may do (just) this problem in groups of up to three people. You will need to write some Runge Kutta code for first order systems!
5.1 11, 13, 18, 21, 22, 26, 31, 35.
solutions8.pdf
Grading: 27 points, distributed as follows:
4.1: 8, 16 = 2 points each; 21a = 1 point; 24, 26 = 2 points each.
4.3: 9 = 8 points
5.1: 13, 18 = 1 point each; 22, 26, 31, 35 = 2 points each.
Due Friday, February 24:
3.6 4, 5, 7, 13, 16, 21, 22.
solutions7.pdf
Grading: 16 points, distributed as follows:
3.6: 4, 5 = 3 points each, 13 = 4 points, 21, 22 = 3 points each.
Due Friday, February 17:
3.5 3, 4, 17, 19, 36, 37, 43, 49, 50, 51, 64.
solutions6.pdf
Grading: 20 points, distributed as follows:
3.5: 3 = 2 points, 17, 19 = 3 points each; 37 = 4 points, 43a, 43b, 49, 64 = 2 points each.
Due Friday, February 10:
3.1 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.
3.4 4, 5, 6, 13, 15, 19, 23.
solutions5.pdf
Grading: 35 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.
3.4: 4 = 3 points, 5, 6, 15 = 2 points each; 19 = 3 points, 23a = 1 point, 23b = 2 points.
Due Friday, February 3: work in the same group as for the Maple project below, and hand in only one assignment per group...recall, groups are optional and consist of from 1-3 people.
2.3 2, 3, 9, 11, 13, 14, 15, 16,17,18.
solutions4.pdf
Grading: 12 points, distributed as follows:
2.3: 2a = 2 points, 2b = 1 point, 9, 11, 13 = 2 points each; 17 = 3 points.
Maple Project 1 due Friday February 3
proj1probs.pdf problems for Maple project 1, due Friday February 3
proj1probs.mws Maple worksheet
numerical1.pdf handout for numerical methods, sections 2.4-2.6
numerical1.mws maple worksheet
2270tut.pdf a brief intro to Maple in the Math Labs which we used in 2270.
2270tut.mws
proj1popans.pdf populations; Investigation C solutions
proj1numans.pdf numerical work solutions
Grading: 32 points, distributed as follows:
1 = 8 points (a,b values = 2 points, line picture = 2 points, solution function P(t) and graph with points = 2 points, year 2025 est = 2 points); 2, 3 = 4 points each; 4a,b,c = 2 points each; 5, 6 = 6 points each; 7 = 4 points.
Due Friday, January 27:
2.1 1, 4, 5, 10, 13, 15, 24
2.2 5, 7, 9, 12, 21, 23, 24
solutions3.pdf
maplesols3.pdf maple used to solve DE's and draw slope fields for hw
maplesols3.mws
Grading: 26 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, 9 = 4 points each (equilibria= 1 point, stability = 1 point, slope field and phase diagram = 1 point, solution formula = 1 point); 21ab = 1 point each; 24 = 2 points.
Due Friday, January 20:
1.3 3, 6, 10, 11, 12, 13, 18, 21, 23, 29.
in 6, also verify (show work) that y(x)=x+C*exp(-x) is the general solution, and compare (for yourself) this formula to the solution curves you sketched. In 18, explain why the existence and uniqueness theorem does not apply for this initial value problem, but then solve this separable equation to show that in fact there exist (at least) two solutions to the given initial value problem.
1.4 9, 12, 19, 22, 35, 41, 43, 46, 54, 60, 66.
1.5 1, 7, 13, 34, 36, 38, 41.
Note that 1.3 #23, 1.4 #46, 60 are now optional.
solutions2.pdf
Grading: 33 points, distributed as follows:
1.3: 6 (verify solution part) = 1 point, 12, 13 = 1 point each, 18 = 3 points (1 point for showing theorem does not apply, 2 points for finding two solutions to IVP), 21 = 2 points.
1.4: 9, 12, 22 = 2 points each; 43, 54 = 2 points each; 66a = 1 point, 66b = 2 points.
1.5: 7, 13, 34 = 2 points each; 38abc = 2 points each; 41 = 2 points.
Due Friday, January 13:
1.1 3, 6, 15, 16, 19, 27, 31, 34, 35, 36;
1.2 6, 7, 13, 18, 19, 21, 25, 29, 33, 34, 39.
solutions1.pdf
Grading: 21 points, distributed as follows:
1.1: 6, 16, 19, 31 = 2 points each; 35, 36 = 1 point each.
1.2: 6, 13, 18, 29 = 2 points each; 34 = 2 points, 39 = 1 point.