Math 2280-1
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Professor Korevaar
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Homework is now due each Monday at the start of class, and solutions should be posted by some time on Tuesday. Assignments are listed below - most recent first. Underlined problems are to be handed in - graded problems will be drawn from these.
Due December 12
9.3 1, 9, 17, 20;
9.4 1, 7, 9, 13;
9.5 1, 2, 7;
9.6 1, 5. (sections 9.5, 9.6 are optional and not on the final exam.)
hwsols14.pdf solutions
Grading: 18 points, distributed as follows:
9.3: 1, 9 = 3 points each; 17 = 2 points; 20 = 3 points;
9.4: 1 = 2 points (no graph necessary); 7, 9 = 1 point each; 13 = 3 points.
Due December 8
7.1 3, 7, 8, 13, 20, 21, 23, 28;
7.2 3, 4, 5, 6, 14, 19, 20, 28, 31;
7.3 3, 7, 8, 17, 20, 31;
7.4 2, 3, 36; (7.4, 7.5 are optional sections)
9.1 6, 7, 10, 13, 15, 17, 20, 30;
9.2 2, 9.
hwsols13.pdf solutions
Grading: 40 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;
7.3: 3, 8 = 1 point each; 17, 20 = 2 points each, 31 = 3 points;
9.1: 6, 10 = 1 point each; 20 = 3 points each, 30 = 4 points;
9.2: 9 = 3 points.
Due December 1
6.3 8, 9, 10, 14, 15, 16, 17; in 8 and 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;
hwsols12.pdf solutions
Grading: 18 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.)
Due November 24
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.)
hwsols11.pdf solutions
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 November 17 Nothing at all! But you have an exam on Friday November 14, covering thru section 5.6.
Due November 10
5.4 : 1, 7, 11, 29. Work 1, 7, 11 by hand (except use technology to draw the phase portrait for 1). You may work 29 by hand, but I'd recommend using Maple to find generalized eigenvectors and chains.
5.5 1, 3, 11, 23, 33, 36 Work all problems by hand except you may have Maple find any eigenvectors you wish. Also have Maple or other tech compute the matrix exponentials as check (and hand this in too).
5.6 1, 13, 15, 19, 23 Do 13, 15 by hand. On 19 and 23 you may use technology to compute variation of parameters formulas for the solutions. the 5.6 hw is due on Wednesday November 12
hwsols10a.pdf solutions for 5.4-5.5.
hwsols10b.pdf solutions for 5.6.
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 November 3
5.2 : 2, 3, 9, 15, 27, 35 You can use Maple for eigenvalues and eigenvectors, and to plot the phase portrait. Actually, pplane makes graphing the phase portrait really really easy, at the URL http://math.rice.edu/~dfield/dfpp.html . Hopefully you can find a printer that lets you print from the pplane applets - The version on the math system, also called "pplane" (which you open from a terminal window by typing pplane into a command line and hitting "return" or "enter"), now works!! On my mac at home, the print option on the applet doesn't work, but I can use the utility "grab" to print or save the window. Here's an example of the phase portrait of an interesting non-linear system, in fact the one which pplane opens with automatically, made on a Math Department machine: pplaneexample.pdf .
(It's a big file and takes a while to load, because of the interesting long solution trajectories.) This system has 4 equilibrium solutions, and near each equilibrium solution the system is well-approximated by the linear theory we're discussing now. But look at all the interesting non-linear theory illustrated in this phase portrait!
5.3 : 3, 7, 9, 14, 16, 17, 21; Also, do the Maple exploration, pages 330-332. Your work begins at the bottom of page 331, "For your personal ....". You'll need to do some derivvation work, pretty much like what we did on October 28. Useful commands can be found in the Maple document posted on our lecture page for October 28th, i.e. oct28maple.mws, oct28maple.pdf, where we worked out a 2-mass, 2-spring system.
hwsols9.pdf
Grading: 26 points, distributed as follows:
5.2: 3, 15, 27, 35 = 3 points each.
5.3: 3 = 2 points; 9, 14, 16, 17 = 3 points each.
quakesols.pdf
Grading: 12 points: 2 points for each step (see solutions)
Due October 27
4.1 : 1, 8, 11, 15, 16, 21a, 24, 26.
4.3 : 9. You may hand in joint work with up to one other person on this problem, which will require you to write some Runge-Kutta code for systems. (Of course, you can help as many people as you want!)
5.1 : 11, 13, 18, 21, 22, 26, 31, 35.
Class problem - added Wed Oct 22. See page 6 of oct24.pdf
hwsols8.pdf
Grading: 31 points, distributed as follows:
4.1: 8, 16 = 2 points each; 21a = 1 point; 24, 26 = 2 points each.
4.3: 9 = 6 points (3 points for each part)
5.1: 13, 18 = 1 point each; 22, 26, 31, 35 = 2 points each.
class problem = 6 points (3 points for each part).
Due October 20
3.5 : 3, 4, 17, 19, 36, 37, 43, 49, 50, 51, 64.
3.6 : 4, 5, 7, 13, 16, 21, 22.
hwsols7.pdf
Grading: 30 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, 13, 21, 22 = 3 points each.
Due October 6
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 September 29
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.
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 September 22
2280maple.html contains your first Maple project. The due date for this project has been extended to Monday September 22.
Grading: 30 points, distributed as follows:
Each problem is worth 3 points for mathematical correctness, for a total of 24 points. A separate score of up to 6 points, is determined by the grader's sense of how well you presented your work.
proj1sols.pdf solutions.
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.
Maple Project grading still to be determined.
Due September 15
2.1 : 1, 4, 5, 10, 13, 15, 24;
2.2 : 7, 9, 12, 21, 23, 24;
hwsols3.pdf
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 September 8 - Monday!
1.3: 3, 6 , 10, 11, 12, 13, 18, 21, 23, 29. In problem 6, consider the actual book problem to be 6a. Then also do
6b Verify y(x) = x+ C*exp(-x) solves the DE, and convince yourself the curves you sketch are consistent with this formula.
6c Use dfield to draw the indicated solution graphs. (For 6a you may use dfield to draw the solution field and then add the solution curves by hand.)
In problem 29, consider the book problem to be 29a. Then also do
29b Get dfield to illustrate several of the non-unique solutions you verify exist in 29a. Recall, you can google "dfield", or go directly to the URL http://math.rice.edu/~dfield/dfpp.html, and click on the "DFIELD 2005.10" button. If you're using the Math Department system the on-line applet won't print hard copies. But, if you open a terminal window and use the command "dfield" a carbon copy of the applet will open, and this copy will let you print hardcopies.
1.4: 9, 12, 19, 22, 35, 41, 43, 46, 54, 66.
1.5: 1, 7, 13, 34, 36, 38, 41.
hwsols2.pdf
Grading: 35 points, distributed as follows:
1.3: 6b (verify solution part) = 1 point, 12, 13 = 1 point each, 18 = 2 points (1 point for showing theorem does not apply, 1 point for finding two solutions to IVP), 29a= 2 points, 29b=1 point.
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 August 29
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 .
Grading: 22 points, distributed as follows:
1.1: 6, 16, 19 = 2 points each; 34, 35, 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). 33 = 1 point, 34 = 2 points, 39 = 1 point.
hwsols1.pdf