Homework Assignments for MATH 3200 ODE (Fall 2007)
Lynn S. Bennethum                        Tues. and Thurs., 10:00-11:15AM, PL 130

Textbook:  Elementary Differential Eqautions, Kohler and Johnsons, 2nd Edition, Pearson Addison Wesley, 2006

Date	What is Due	Notes
Tues.  Dec. 11	Final Exam   10am-noon PL 130 Over all material covered in class, through Section 5.6	2 sides of an 8.5"x11" paper will be allowed for notes.  No technology.
Thurs. Dec. 6	NOT to be turned in (solutions will be given): Section 5.5: 1, 7, 11, 20 Section 5.6:  3, 7, 19 Section 5.7: 1a, 1c, 15	We will omit Section 5.4
Thurs. Nov. 29	Section 5.1:  1, 6, 9, 22 Section 5.2:  1, 3, 5, 6, 13, 16, 19, 23, 24, 43 (use partial fraction decomposition). Section 5.3:  3, 7, 11, 12, 27, 28	If the Laplace transform does not exist, just state it - you do not need to prove it.
Thurs. Nov. 15	EXAM 2  Over material from Chapters 3 and 4. One side of 8.5" and 11" sheet of paper allowed for notes.  No technology.	No homework will be due.
Thurs. Nov. 8	Section 4.5:  Extra problem for 4.5 (below) Section 4.6:  3, 8, 11, 19, 24, 33, 34, 36 Section 4.7:  3, 8, 16, 19, 29
Thurs.  Nov. 1	Section 4.3:  3, 6, 8, 11, 16, 19 Section 4.4:  3, 8, 13, 16, 19, 28 Section 4.5:  3, 4, 8, 11	Hint:  For 16 of Section 4.3, the solutions do form a fundamental set.
Thurs. Oct. 25	Section 3.8:  5, 12, 20, 34, 36 Section 4.1:  2, 5, 7, 8, 10, 13, 15, 17, 20, 26 Section 4.2:  3, 4, 5, 7, 9, 12, 13, 15 From linear algebra:  review how to find eigenvalues and eigenvectors.	Answer for 34 of Section 3.8:  omega>1.
Thurs. Oct. 18	Section 3.6:  3, 8, 10    Extra credit (4 pts):  11   Section 3.7:  3, 6, 9, 13, 15, 22 Start reviewing linear algebra:  multiplying matrices, adding matrices, determinant, and inverses of 2x2 matrices.	Note:  For problem 11 of Section 3.6,  I did not get the answer in the back of the book.
Thus. Oct. 11	Section 3.2:  3, 5, 8, 13, 18 Section 3.4:  1, 4, 11, 15 Section 3.5:  1b,c;  2a,b;  5, 8, 16, 25
Thurs. Oct. 4	ODE PROJECT 1 Due Section 3.1:  2, 3, 5, 6 (use Theorem 3.1) Section 3.3:  1, 4, 7, 14, 16	Section 3.2 homework will be due next week.
Thurs. Sept. 27	HW:   Nothing needs to be turned in (concentrate on studying for exam).  To review for the exam:  Section 2.10:  5, 11 Practice problems for exam (to be handed out) Chapter 2 Review Exercises (p. 100-101). EXAM 1  Over material through Section 2.10.   One side of an 8.5"x11" paper will be allowed for notes.  No technology.	Homework for Section 2.10 will not be turned in.  Solutions will be handed out on Tuesday.
Thurs. Sept . 20	HW: Section  2.6:  3, 4, 7, 10, 13, 19, 24 (hint:  use int(du/(a^2+u^2)) = 1/a arctan(u/a) + C) Section 2.7:  1, 4, 7, 23a, 24a Section 2.8:  World Population Problem (given below), 1, 2, 3, 5, 10 (note that we do not try to solve problems 5 and 10 - we only look at the direction fields to get the information)
Thurs.  Sept. 13	HW: Section 2.3:  2, 3, 6, 11, 16, 23 Section 2.4:  1, 2, 3, 10 (also, give a physical interpretation to k>0, k<0, M>0, M<0), 13 Section 2.5:  3, 4, 15, 16
Thurs. Sept. 6	HW: Section 1.3:  1, 4,  9, 11 (different from textbook answer), 12, 14-19 Section 2.1: 1, 2, 3, 4, 8, 11a, 13a, 13b, 14, 15, 17 Section 2.2:  1, 12, 17, 20, 21, 28 (Hint:  Look at the sign of y'), 34, 41	Problems in red are modified from original handout sheet.
Thurs.  Aug.30	HW: I.  Pick out 10 functions to differentiate and 10 functions to integrate and proceed to differentiate and integrate them by hand.  Be sure to write out all your work. II  Problems from Section 1.2:  1, 2, 3, 4, 11, 16, 20, 21, 24


World Population Problem:  (Bill Briggs)
As you may know the world population reached 6 billion in (assume January) 2000 and was growing
at a rate of 1.2% per year. Assuming that growth rate remains constant, determine the
function that describes the world population growth for all times after 2000. According
to this function, when will the population reach 7 billion? According to this function,
how many people were added (net gain) in 2007? How many people will be added (net
gain) in 2010? What is the doubling time of the world’s population assuming that the
growth rate remains constant? If you assume that the human race began with two
individuals, what date does this model give for the “creation”? Is the model accurate?
Why or why not?  

Extra Problem for Section 4.5:  
Consider the system
          y'_1 = -y_2                        
          y'_2 = -y_1.  
The eigenvalues are 1 and -1, and the eigenvectors are [1,-1] and [1,1] respectively.  Sketch the phase plane:

1. Determine where the slopes are zero, are they going right or left?
2. Determine where the slopes are undefined, are they going up or down?
3. Sketch the lines representing constant multiples of each eigenvector.  For each eigenvector, does the solution go in toward the origin, or out away from the origin?
4. Sketch a few arrows between each of these 4 lines.
5. Sketch the solution curve for the following initial conditions:  [y_1(0),y_2(0)] = [-2,-1], [1,2], [2,1], [-1,-2] 

Week of	TENTATIVE Class Schedule
Aug. 20	Review differentiation and integration Sections 1.1, 1.2
Aug. 27	Sections 1.3, 2.1, 2.2
Sept. 3	Sections 2.3, 2.4, 2.5
Sept. 10	Sections 2.6, 2.7, 2.8
Sept. 17	Sections 2.10, 3.1, 3.2
Sept. 24	Section 3.3  and review   EXAM 1:  Material through 2.10 One side of an 8.5x11" sheet of paper will be allowed for notes No technology
Oct. 1	Sections 3.4, 3.5, 3.6     PROJECT 1 is due
Oct. 8	Sections 3.7, 3.8, (3.9)
Oct. 15	Sections (3.10), 4.1, 4.2
Oct. 22	Sections 4.3, 4.4, 4.5
Oct. 29	Sections 4.6, 4.7,( 4.10)
Nov. 5	Sections 5.1, 5.2, 5.3
Nov. 12	Section (5.4) and review EXAM 2:  Material from Chapters 3 and 4 One side of an 8.5x11" sheet of paper will be allowed for notes
Nov. 19	FALL BREAK
Nov. 26	Sections 5.5, 5.6, 5.7
Dec. 3	Catch up and Review PROJECT 2 is due
Dec. 10	FINAL EXAM - exact date, time, and location to be announced.