Math 2250-1
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Professor Korevaar
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Homework is due each Friday by 5:00 p.m. If you do not hand in homework immediately after class, please bring it by the Math main office JWB 233 and leave it with Paula Tooman at the front desk. (This replaces the earlier instructions to leave homework in my mailbox.) Alternately, you can drop it by my office in LCB 204, and slide it under the door if I'm not in.
Assignments are listed below. Underlined problems are to be handed in - graded problems will be drawn from these.
Solutions should usually be posted by the Monday after an assignment is collected.
Due December 12 Last assignment, hurray!
9.1: 5, 8, 11, 15, 20, 24;
9.2: 5, 6, 7, 8, 9, 14, 15, 19, 27, 30; on 19, 27 use pplane to find and classify the other equilibrium solutions besides (0,0), and print out a phase portrait with representative solution trajectories. (google "pplane", or go directly to http://math.rice.edu/~dfield/dfpp.html and click on the PPLANE 2005.10 icon ... it's a Java applet, or use the Math Department version which will let you print without taking a screenshot ... you open it on a Math machine, with the command "pplane &", followed by enter or return, in a terminal window.)
9.3: 8, 9, 10, 14, 15, 16, 17; on 8, 10 use pplane to create a phase portrait for the nonlinear system (3) and explain how your linearization compares to this phase portrait near the equilibrium solution you're studying.
9.4: 12, 14, 14, 15, 16;
Despite what the text problems may ask for, the only pplane (or other) pictures you need to hand in are the ones I ask for above. (But it's probably fun to look at the others anyway.)
hwsols15.pdf solutions
Grading: 37 points, distributed as follows:
9.1: 5, 8, 11 = 1 point each; 15, 20 = 2 points each; 24 = 1 point;
9.2: 6, 8, 9 = 1 point each; 19 = 2 points, 27 = 3 points (pplane analysis is part of 19, 27), 30 = 3 points;
9.3: 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. ;
9.4: 12, 14 = 3 points each (2 points for linearization, 1 point for understanding nonlinear equilibria in these difficult borderline cases).
Due December 10 (Wednesday)
7.4 exploration about the 7 story building shaken by an earthquake, see our Maple page.
Grading: 18 points: 3 points for each of 6 problems.
Due December 5
7.4: 2, 3, 8, 13, 14, 16, 17, 18;
7.5: 5, 6, 10, 15, 16, 19. (this section is not required.)
hwsols14.pdf solutions
Grading: 15 points, distributed as follows:
7.4: 2, 8, 13, 14, 18 = 3 points each.
Due December 2 (Tuesday)
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.
hwsols13.pdf solutions
Grading: 38 points, distributed as follows:
7.1: 8, 18, 21a, 24, 26 = 2 points each.
7.2: 9, 10 = 1 point each, 14, 21 = 3 points each, 23 = 2 points.
7.3: 4, 6 = 3 points each; 14, 25, 30 = 4 points each.
Due November 21
6.1: 7, 17, 18, 24, 29 ;
6.2: 4, 10 19, 28;
6.3: 5, 15, 26, 31, 32, 41;
hwsols12.pdf solutions
Grading: 25 points, distributed as follows:
6.1: 7 = 2 points, 18, 24 = 3 points each, 29 = 2 points.
6.2: 4, 10 = 2 points each, 19 = 3 points.
6.3: 5, 15, 26, 32 = 2 points each.
Due November 14
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;
10.4: 2, 3, 9, 10, 15, 16, 29, 36;
10.5: 7, 13,, 31, 34.
hwsols11.pdf solutions
Grading: 35 points, distributed as follows:
10.1: 3, 8, 13, 20, 23, 28 = 1 point each.
10.2: 4, 6 = 2 points, 14 = 3 points, 20 = 2 points.
10.3: 8 = 1 point, 17, 20, 31 = 2 points each.
10.4: 2, 10, 16, 36 = 2 points each.
10.5: 7 = 2 points, 34 = 3 points (no graph necessary).
Due November 7
Maple project II: go to the Maple page for details
5.5: 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.
hwsols10a.pdf 5.5 and 5.6 solutions
hwsolsEP3.7.pdf EP3.7 solutions
project2sols.pdf Maple project solutions
Grading: 22 points, distributed as follows:
5.5: 49 = 2 points
5.6: 3, 7, 14 = 3 points each, 21, 22 = 2 points each.
EP 3.7 3 = 3 points, 7 = 2 points, 11 = 2 points: phase amplitude form not graded, just values of A, B in A*cos(2t)+B*sin(2t).
Maple project: 24 points: 3 points each for exercises 1-6. Plus up to 6 points for clarity of exposition. (So you will receive two scores, with a total which can be as high as 24.)
Due October 31
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, just find the actual solutions x(t) in linear combo form, and then put them into phase-amplitude form.)
5.5: 3, 4, 12, 13, 19, 34, 37, 43, 49, 50, 52. Problems 49,50,52 (variation of parameters) are postponed until next week.
hwsols9.pdf
Grading: 40 points, distributed as follows:
5.2: 2, 9, 13, 22 = 2 points each.
5.3: 10 = 2 points, 22 = 3 points, 33 = 2 points, 37 = 3 points.
5.4: 4, 15, 17, 18 = 2 points each. 5.5: 3 = 2 points, 12, 19, 34, 37 = 3 points each.
Due October 24
4.4: 1, 2, 3, 6 8, 9. 11. 13. 26;
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 or 4.7 problems, where appropriate.
5.1: 2, 9, 11, 17, 27, 29, 30, 31, 34, 35, 39.
hwsols8.pdf
Grading: 28 points, distributed as follows:
4.4: 2, 3, 6 = 1 point each; 9, 11, 26 = 2 points each.
4.7: 2, 5, 7, 13, 15, 17 = 1 point each; 21, 23, 25 = 2 points each.
5.1: 2, 11 = 2 points each; 27, 34, 39 = 1 point each.
Due October 20
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: 27 points, distributed as follows:
4.1: 7 = 1 point, 10 = 2 points, 16 = 1 point; 19, 22, 26, 31 = 2 points each, 33 = 1 point.
4.2: 6, 18, 27 = 2 points each; 9 = 1 point.
4.3: 1, 3, 6 = 1 point each; 9, 10 = 2 points each.
Due October 3
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 (x1 in 32) with Cramer's rule. Then compute A^(-1) with adjoint formula (page 210), 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.
4.1: 1, 7, 9, 10, 15, 16, 19, 22, 25, 26, 31, 33; Section 4.1 homework is postponed until October 10.
hwsols6.pdf
Grading: 24 points, distributed as follows:
3.5: 7, 13, 23 = 2 points each; 30, 32 = 1 point each.
3.5: tech checks on 22, 23 = 2 points each. 3.6: 6, 17 = 2 points each; 22, 32 = 4 points each.
Due September 26
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;
Grading: 30 points, distributed as follows:
3.1: 4, 17, 19, 23, 29 = 2 points each;
3.2: 8, 9 = 1 point each, 17 = 2 points.
3.3: 13 = 1 point, 20 = 3 points, 34 = 1 point:
3.4: 5, 7, 10, 13, 19, 31a,b, 34, 39, 40a,b = 1 point each;
hwsols5.pdf
Due September 22
Math 2250-1 maple page contains your first Maple project, which is due on September 22. (It was originally due September 19.)
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.
Due September 19
2.3: 2, 3, 9, 10, 12, 17, 18;
2.4: 5;
2.5: 5, 25;
2.6: 5;
Grading: 14 points, distributed as follows:
2.3: 3, 10, 12 = 2 points each;
2.4: 5 = 2 points;
2.5: 5, 25 = 2 points each;
2.6: 5 = 2 points.
hwsols4.pdf
Due September 12
1.5: 36, 38, 41;
2.1: 1, 3, 6, 8, 9, 11, 12, 22, 33;
2.2: 5, 7, 9, 12, 14, 15, 23.
Grading: 21 points, distributed as follows:
1.5: 36a = 1 point, 36b = 2 points, 41a = 1 point, 41b = 2 points.
2.1: 8 = 3 points, 12, 22 = 2 points each;
2.2: 7, 14 = 2 points each, 23a, 23b = 2 points each.
hwsols3.pdf
Due September 5
Maple Introduction: Go through the notes posted at our Maple page, Math 2250-1 maple page , in Maple! (Nothing to hand in.)
1.3: 3, 8, 11, 12, 13, 14, 21, 24 ; Use the applet "dfield" for 8, 24. You can google it, or just follow this link: http://math.rice.edu/~dfield/dfpp.html, and click on the "DFIELD 2005.10" button. This applet will not print if you're on the Math Department system - to get a carbon copy that will, use the command "dfield" in a terminal window.
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. LATE NOTE: The due date for 36, 38, 41 is now extended until next Friday, September 12.
Grading: 20 points, distributed as follows:
1.3: 8, 12, 14, 24 = 2 points each;
1.4: 4, 9, 20, 40 = 2 points each;
1.5: 8, 13 = 2 points each.
hwsols2.pdf
Due August 29
1.1: 3, 4 7 , 15, 16, 19, 20, 27, 30, 34, 36, 46.
1.2: 5, 7, 10, 14, 19, 20, 25, 26, 36, 44 .
Grading: 23 points, distributed as follows:
1.1: 7, 16, 20 = 2 points each; 30, 36 = 1 point each.
1.2: 7, 10, 14 = 2 points each; 20 = 3 points: 2 points for roughly accurate sketch, 1 point for correct values of x(5) and x(10). 26, 36, 44 = 2 points each.
hwsols1.pdf