Homework

Math 210

Spring 2005

Professor Donnay

 Spring 2005:

Home work Redos: you can redo any problem you did not know how to do or that you got wrong and resubmit it the following week. You will get full credit for the corrected work. Attach the corrections to the old hw.

Wk	Due	Section	Problems
1	Wed Jan 18		fill out and return information survey part 1 and part 2.
	Mon Jan 23; Extension given till Wed Jan 25	1.1	1, 2, 3bc, 6, 10, 11, 18 Make an estimate of the carrying capacity of the earth: i.e. how many people can the earth sustain. Explain your assumptions and reasoning. (To be handed in separately from the other hw).
	Wed Jan 25:	Wk 1Collapse	Read through the end of Chapter 1 (to p. 75)
Wk 2	Wed Jan 24		Finish the worksheet on Long Term Behavior and Sensitive Dependence.
	Mon Jan 30	1.3	5, 7, 9, 11*, 12, 14*, 15, 17* and supplemental sheet involving Sect 1.1, 1.5, 1.6. * indicates more challenging problem. This hw is due by 4pm on Monday Jan 30. Please hand in to Kiki Kemp in our class.
	Wed Feb 1	Wk 2 Collapse	To the end of Ch 3
Wk 3	Mon Feb 6	1. 4	3, 4
	Mon Feb 6	1. 6	2, 14, 30, 33, 34, 36, 37, 38*, 39. Also please do the attached mini-quiz: it is closed book and does not count for your grade but will give you feedback on how you are doing. Use up to 25 minutes. Have a calculator. Hand this in separately from your homework. This is some of the basic material from Sect 1.1 that you should know at this point.
	Wed Feb 8		Hw redos from wk 1 and wk 2 are due.
	Wed Feb 8	Collapse	To the end of Ch 4
Wk 4	Mon Feb 13	1.2	5, 8, 9, 23, 33, 35 (I am removing #31 from the hw list) Finish mixing problem from class. Correct and resubmit last week’s quiz if it was not perfect. Do harvesting problem; write up neatly; be prepared to have it reviewed by a classmate. Note – if you were not in class on Wed, you become a person 4.
	Wed Feb 15		Hw redo from Wk 3 is due. Harvesting paper rewrite due as well as 2^nd harvesting problem. See Play-by-Play for handouts.
	Friday Feb 17	Collapse	To the end of Ch 5.
Wk 5	Monday Feb 20		Homework outlined on sheet. Here are some hints for solving the logistic equation via partial fractions. Section 1.7 #7: think of our discussion of shifting the function f(y) up or down as the parameter changes. Extra credit challenge: Solve the logistic equation for general values of k and N.
	Wed Feb 22		Hw redo for Wk 4 is due.
	Friday Feb 24	Collapse	To the end of Ch. 6
Wk 6	Mon Feb 27		Midterm is due.
	Friday March 3	Collapse	To the end of Ch. 7
	Spring Break
Wk 7	Wed March 15	Sect. 1. 5	#14, 16 #2, 9, 10, 12,
	Wed March 15	Sect. 1. 8	#7, 12, 13, 9, 19, 20, 21, 23, 29. Hints for S1.5 and S1.8
	Friday March 17	Collapse	To the end of Ch. 9
Wk 8	Wed March 22	Sect. 2.1	8(do B and D), 9i, 10i, 15*
	Wed March 22	Sect. 2.2	6, 10, 11acd – consider equilibrium points, 13, 16, 21
	Wed March 22	Sect 2.3	1, 2, 5, 7, 8a.
	Friday March 24	Collapse	To the end of Ch. 11.
Wk 9	Wed March 29	Ch 2	Sect 2.1 #17(draw this using system solver); Sect 2.2 #15; Sect 2.3 #10
	Wed March 29	Sect 3.1	# 5, 6, 8, #(20-23)*, 25a, linearity problem from class Use this linearity result to show that if v is an eigenvector for a matrix transformation A, then (k v) is also an eigenvector for A, wher for k=constant.
	Wed March 29	Sect 3.2	#3ab, 6ab – for these two, Give a specific value for the eigenvectors in addition to the general relation. #16, 17.
	Friday March 31	Collapse	To the end of Ch. 13
Wk 10	Wed April 5	Sect 3.2	#3c(print this out and hand in)de, 6cde – for these two systems, also solve the initial value problem Y(t=0) = (1,2).
	Wed April 5	Sect 3.3	#3, 4 Draw the phase portrait based on your eigen analysis (not by looking at the computer program). When you are done, check whether your drawing is correct by using the computer. If you drawing is wrong, correct it and explain what your mistake was.
	Wed April 5	Sect 3.1	Redo: #20, 21, 22, 23. Linear approximation worksheet for a function f(x,y) of two variables.
	Mon April 3 or Wed April 5		Mini-quiz on eigenvalues and eigenvectors
	Friday April 7	To the end	To the end of Ch. 14.
Wk 11	Wed April 12	Sect 3.4	1, 3, 4, 5, 10
	Wed April 12	Sect 3.5	13, 23
	Wed April 12	Ch. 3 Review exercises	Do one of #27, 28 or 32. If you are confident in your ability to calculate eigenvalues and eigenvectors, you can use Mathematica. Else do the eigen-calculations by hand.
	Wed April 12		Population problem Also: hand in a note saying what project you want to work on and possible people to be your partner (if you have someone).
	Friday April 14	Collapse	To the end of Ch. 15
Wk 12	Monday April 17	Sect 5.1	Homework on linearizations For Monday, you should write up a list of topics that could be covered on the test and hand this in. This test will cover everything since the last test. This starts with Sect. 1.8 (linear equations) and goes thru Sec. 5.1 (non-linear systems). Also on Monday, hand in a list of problems you would like me to go over in the review session in class on Wed (the first half of the class). As part of the test, I might ask you to give a couple of examples from the book Collapse that relate to mathematics we hve studied in the course and explain the connection.
Wk 13	Wed April 26		Midterm is due
	Friday April 27		Finish reading Collapse and final post.

 Home from spring 2003 course.

Wk	Due	Section	Problems
1	Thur Jan 22		Find an example of a Differential Equation
2	Tue Jan 28	1.1	Hand in your example of DE. Write a short paragraph saying how good is the population model when compared with the actual data in Table 1.1. #4, 8, 9,
	Tue Jan 28	1.2	1, 3, 4
3	Thur Feb 6	1.1	3, (do not need to do 4 - already did it last week).
		1.3	3, 10, 12, 13, 15, 16, 17,
		1.4	3
		1.6	2: Find the equilibrium values and determine if they are sinks or sources. Don't do anything about "phase line".
		1.6	3, 6, 7, 8 (see book for description of "phase line"; basically, it is a one dimensional diagram that shows equilibrium points and whether slope is going up or down). 14, 15, 18, 19, 20, 30, 31 ,33, 35, 37
			Review for Thur your basic integrations methods: x^n, 1/x, substitution.
4	Thur Feb 13	1.2	7, 9, 10, 13, 16, 20, 27, 29, 33, 35, 36, 37, Feel free to use your Detool programs to get graphical information about the problems to check against your analytic results.
5	Thur Feb 20	1.5	#2, 3, 9, 12, 13, 14. For #13, also make graphs of the functions y(t) = e^(-1/t), y(t) = 2e^(-1/t), and y(t) =ce^(-1/t).
6	Thur Feb 27	Appendix A	1, 4 :solve these 2 both by undetermined coefficients and by integrating factor (if you can!). For each example, which method did you finder easier; explain in a paragraph. 5, 9, 11 (this question shows that we can "add" guesses) , 12, 14, 15 (These two problems are examples of what #11 is talking about). Solve y' + 4 y = 3 exp(-4t), y(0) = 5. Make up examples of 1^st order differential equations that are: (a) linear, (b) non-linear, (c) linear, non-constant coefficients, (d) linear, constant coefficient, (e) linear, non-constant coefficients, non-autonomous, (f) linear, constant coefficient, non-autonomous, (g) linear, constant coefficient, autonomous. For (e,g) make both a homogeneous and a non-homogeneous example.
		1.8	2
7	Thur March 6		7, 9, 13, 26, 28 - First set p=2 lbs per minute and find the formula for the amount of sugar as a function of time in this special case. What is the concentration of sugar in the tank the instant before the tank becomes empty?. At what time does the tank become empty. Then go on to do the stated problem with the general value p. Remember p is some constant value.
			Find and hand in article from web about the fishing industry (try Lexus at Library site for example), write a short summary of article and propose a new strategy for the fishing industry.
8	Thur March 20		Mid-term rewrite. See course home page.
		1.7	1, 3 (will have 2 bifurcation values, use quadratic formula), 7, 9, 12, 15ab.
		2.1	1, 2(ii), 3(ii) - preditator extinct means y(0)=0, 5(ii), 7a, 15, 17
		2.2	9 (photocopy the picture or trace over it)
9	Thur March 27	2.2	1ab, 5ab , 10 (photocopy the picture or trace over it), 11
		2.2	17, (Challenge problem: 20)
		2.3	3, 4, 5, 7, 8, 9, 10, 11a.
10	Thur April 3	2.1	8 (due pts A, B), 16, 19 (you must check that sin(t) solves the DE and also satisfies the initial conditions. Also translate the equation into a system)
		2.2	7a, 8a, 13, 14, 15, 16, 23, 24, (use the DE Sketchpad to help visualize these). Challenge Problem: 27
		3.1	5, 8, 16
		3.1	26
		3.2	1, 3, 13a (first find eigenvalues, eigenvectors, solutions Y1(t), Y2(t)). Link to Lab 4 - instructions for Mathematica Eigenvalue, vector. (feedback - hard and long).
11	Tues April 8	(3.1 mistake) Should be 3.2	Compute eigenvalues, eigenvectors by hand now. 1a,b 6abe and write formula for Y1(t), Y2(t). Plot Y1(t), Y2(t). 11ab (first find eigenvalues, eigenvectors)
		3.3	1 (you will need to do 3.2 # 1 first), 4 (you will need to do 3.2 #6 first) 9 (draw solution curves for S3.2 #11ab and also draw general phase portrait).
12	Thur April 17	Appendix B	Do Complex Numbers Review worksheet (see Appendix B for review).
		3.2	8ab, 13 -find eigenvalues, vectors, draw phase portrait. You do not have to solve the initial value problem.
		3.3	6
13	Thur April 24	3.4	1, 4,6, 10ab,12ab, 23.
		7.2	1 (optional #2 if you want more practice). You do not have to compare these with Euler method.
14	Thur May 1	2.4	#1ab(only do it for t from 0 to 2 ).
		3.6	Take the equations from #9,16. For these 2^nd order equations, write as a 1^st order system. Then calculate eigenvalues, eigenvectors, write general solution. Sketch phase portrait. Then solve for particular solution satisfying given initial condition.For #9, solve initial condition (y(0)=3, y'(0)=-3) Include this solution on your phase portrait. For the particular solutions, also draw the (t, y(t)) graph and the (t, y'(t)=v(t)) graph. Check your answers by using HPGSystemSolver.
		5.1	1, 3 (calculate the equilibrium points yourself)-also draw the global phase portrait for this example by combining the linear pictures. Check your picture by using HPGSystemSolver. #7 - just calculate the equilibrium points.