Winter 2003-2004 Math 222 Tentative Syllabus

Date	RQ	Section	Homework
Week 1
M 1 Dec		6.2	Practice: 6.2 #3,17,23,25
			Turn in: 6.2 #4(H)1,10(H),18,24,26,*352
T 2 Dec		7.1	Practice: 7.1 #3,9,13,21
			Turn in: 7.1 #8,14,22(also plot a phase plane portrait),24,*25,26
R 4 Dec		Lab	Trajectories of Linear Systems: All Parts
			Turn in: all assigned parts of the lab
F 5 Dec		7.2	Practice: 7.2 #3,11,13,15,29
			Turn in: 7.2 #12,22,32(write the solution in terms of x1, x2, x3, and x4)3
			Turn in: also do these problems on modeling with systems of DE's.
Week 2
M 8 Dec		7.3	Practice: 7.3 #3,9,25,33,35
			Turn in: 7.3 #6(H),8(H),26,*344,*365 (Use the eigenvalue method and show all steps for all problems. Find real-valued solutions to all problems.)
T 9 Dec		Quiz	Turn in HW from 6.2, 7.1, 7.2, modeling with systems of DE's, and the Trajectories of Linear Systems lab. (Please turn in the lab using the electronic drop box.) (Directions for the drop box.)
		7.6	Practice: 7.6 #1,10,12,16
			Turn in: 7.6 #5(H),13,15,21
			Special Instructions: For the problems marked (H), you may use a calculator (not a programmable one) but do not use Maple. For the other problems, you may use the Maple code from class.
R 11 Dec		Lab	Lead in the Body: All Parts
			Turn in: all assigned parts of the lab
F 12 Dec		9.1; 9.2	Practice: 9.2 #1,2,3,7,8,9,13 (Use the instructions below.)
			Turn in: 9.1 #7,11; 9.2 #5,17 (For #5 and #17 classify the critical point using eigenvalues and eigenvectors. Make sure you classify any nodes as proper or improper. Confirm your answers using a phase plane portrait.)
			Turn in: also do these problems on equilibrium solutions to nonhomogeneous systems of DE's.
Week 3
M 15 Dec		Review
T 16 Dec		Exam 1	Turn in HW from 7.3, 7.6, 9.1, 9.2 #5 and #17, equilibrium solutions to nonhomogeneous systems of DE's and the Lead in the Body lab. (Please turn in the lab using the electronic drop box.)
R 18 Dec		Lab	Predator-Prey Models: All Parts (including those marked optional)
			Special Instructions: For Part 5, #2 try the following two changes to the model: (a) Suppose that the prey is ``stocked'', that is, extra individuals are added to the population, at the rate of 20 per year. (b) Suppose that poison is put out to kill the predators, and in fact kills 5% of each species per year. (In particular, find the new equilibrium.)
			Turn in: all assigned parts of the lab
F 19 Dec		9.2; 9.3	Practice: 9.2 #19,21,23,27,31
			Turn in: 9.2 #25,29; 9.3 #1,6,8,13,17. For each of the problems in 9.3, also explain the behavior near the equilibrium point in terms of the predators and the prey.
			Winter Break
Week 4
M 5 Jan		10.1	Practice: 10.1 #3,7,9,13,27
			Turn in: 10.1 #6(H),10(H),21(H),31(H),*38
T 6 Jan		Quiz	Turn in HW from 9.2, 9.3, and the Predator-Prey Models lab. (Please turn in the lab using the electronic drop box.)
		10.2	Practice: 10.2 #3,5,11,13
			Turn in: 10.2 #9(H)6,12,14
R 8 Jan		Lab	Experiments With the Laplace Transform: Parts 1-2
			Turn in: all assigned parts of the lab
F 9 Jan		-	Class cancelled (to be made up later)
Week 5
M 12 Jan		10.2	Practice: 10.2 #17,21
			Turn in: 10.2 #18(H),20,23
			Turn in: also do these problems on nonhomogeneous systems of DE's.
T 13 Jan		Quiz	Turn in HW from 10.1, 10.2 #9,12,14, and the Experiments With the Laplace Transform lab. (Please turn in the lab using the electronic drop box.)
		10.3	Practice: 10.3 #1,9,13,19,27
			Turn in: 10.3 #3(H),15(H),17(H),21(H),37(H),*40
R 15 Jan		Lab	Damping and Resonance Investigations Using Laplace Transforms: All Parts
			Turn in: all assigned parts of the lab
F 16 Jan		10.4	Practice: 10.4 #1,5,7
			Turn in: 10.4 #6(H)7,13(H),*36
Week 6
M 19 Jan		10.4;10.5	Practice: 10.4 #15,19,23
			Turn in: 10.4 #17(H),21(H),27(H)8
T 20 Jan		Quiz	Turn in HW from 10.2 #18,20,23, 10.3, 10.4 #6,13,36, nonhomogeneous systems of DE's, and the Damping and Resonance Investigations Using Laplace Transforms lab. (Please turn in the lab using the electronic drop box.)
		10.5	Practice: #7,13,25,29,31
			Turn in: 10.5 #2(H),21(H),*289,33
			Turn in: also do these problems on discontinuous forcing functions.
R 22 Jan		Delta Function	Turn in: these problems on periodic or impulse forcing functions.
F 23 Jan		Taylor Series	Turn in: these problems on Taylor series and geometric series.
Week 7
Su 25 Jan			Cancelled
M 26 Jan		Review
T 27 Jan		Exam 2	Turn in HW from 10.4 #17,21,27, 10.5, discontinuous forcing functions, periodic or impulse forcing functions, and Taylor series and geometric series.
R 29 Jan		11.1	Turn in: these problems on convergence of series and operations on series.
F 30 Jan		Lab	Taylor Polynomials II: Parts 1-5, Part 6 #1-7
			Special Instructions: For Part 6, also answer the following: 5(b). Use the ratio test to give absolutely conclusive evidence for your answer to #5. (Extra problem 7(b) has been removed from the assignment.)
			Turn in: all assigned parts of the lab
Week 8
M 2 Feb		11.1	Practice: 11.1 #3,5,7,13,21
			Turn in: these problems on power series solutions of DE's.
T 3 Feb		Quiz	Turn in HW from convergence of series and operations on series and the Taylor Polynomials II lab. (Please turn in the lab using the electronic drop box.)
		IX.1	Practice: IX.1 #910,1311,1912
			Turn in: IX.1 #10(H),12(H),23 (Find enough terms to see the pattern; at least through a2 and b2. Don't forget the sketches.13)
R 5 Feb		Lab	Experiments with Fourier Series: Parts 1-3, Part 5 #1-4
			Turn in: all assigned parts of the lab. Other parts may be turned in for Extra Credit.
F 6 Feb		IX.2	Practice: #314,15(a),16(a)
			Turn in: IX.2 #2(H),10,11 (Find enough terms to see the pattern; at least through a2 and b2. Don't forget the sketches.15)
Week 9
M 9 Feb		IX.3	Practice: IX.3 #116, 717
			Turn in: IX.3 #5(H),8,9 (Find enough terms to see the pattern; at least through a3 or b3. Don't forget the sketches.18)
T 10 Feb		Quiz	Turn in HW from power series solutions of DE's, IX.1, IX.2, and the Experiments with Fourier Series lab. (Please turn in the lab using the electronic drop box.)
		IX.3	Practice: IX.3 #1219,1320
			Turn in: IX.3 #1121,*15
			Turn in: also do these problems on Fourier series.
R 12 Feb		Lab	Review of Fourier Series: Parts 2-4
			Turn in: all assigned parts of the lab.
F 13 Feb		IX.4	Catch up on homework.
Week 10
M 16 Feb		IX.4	Practice: #122,723,824,925
			Turn in: IX.4 #3,10,11(be careful!),*17(you may leave your answer to (a) in the form xsp(t) = $${\frac{{a_0}}{{2}}}$$ + $$\sum_{{n=1}}^{{\infty}}$$$$\left[\vphantom{ a_n \cos(n\pi t) + b_n \sin(n\pi t) }\right.$$ancos(n$$\pi$$t) + bnsin(n$$\pi$$t)$$\left.\vphantom{ a_n \cos(n\pi t) + b_n \sin(n\pi t) }\right]$$)26
T 17 Feb		Chaos	Turn in HW from IX.3 and Fourier series, and the Review of Fourier Series lab. (Please turn in the lab using the electronic drop box.)
R 19 Feb		Review	Bring laptops for course evaluations.
F 20 Feb		Exam 3
Finals Week
Su 22 Feb		Review	Review session: 4:00-5:00 p.m., G310
M 23 Feb		-	Final Exam: 8:00 a.m., G219 and G221