MATH 3200 Homework

Homework Problems:

Section 1.2: 1, 2, 3, 4, 11, 16, 20, 21, 24
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
Section 2.3: 2, 3, 6, 11, 16, 23
Section 2.4: 1, 2, 10 (also, give a physical interpretation to k>0, k<0, M>0, M<0), 13
Section 2.5: 3, 4, 15, 16
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, 23ab, 24ab

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)
Section 2.10: 5, 11
Section 3.1: 2, 3, 5, 6 (use Theorem 3.1)
Section 3.3: 1, 4, 7, 14, 16
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
Section 3.6: 3, 8, 10 Extra credit (4 pts): 11
Section 3.7: 3, 6, 9, 13, 15, 22
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
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
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
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
Section 5.5: 1, 7, 11, 20
Section 5.6: 3, 7, 19
Section 5.7: 1a, 1c, 15

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:

Determine where the slopes are zero, are they going right or left?
Determine where the slopes are undefined, are they going up or down?
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?
Sketch a few arrows between each of these 4 lines.
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

Jan. 20

Review differentiation and integration
Sections 1.1, 1.2

Jan. 26

Sections 1.3, 2.1, 2.2

Feb. 2

Sections 2.3, 2.4, 2.5

Feb. 9

Sections 2.6, 2.7, 2.8

Feb. 16

Sections 2.10, 3.1, 3.2

Feb. 23

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

March 2

Sections 3.4, 3.5, 3.6
PROJECT 1 is due

March 9

Sections 3.7, 3.8, (3.9)

March 16

Sections (3.10), 4.1, 4.2

March 23

SPRING BREAK

March 30

Sections 4.3, 4.4, 4.5

April 6

Sections 4.6, 4.7,( 4.10)

April 13

Sections 5.1, 5.2, 5.3

April 20

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

April 27

Sections 5.5, 5.6, 5.7

May 4

Catch up and Review
PROJECT 2 is due

May 11

FINAL EXAM - exact date, time, and location to be announced.

Date	What is Due	Notes
Mon. May 11	Final Exam. Time and location to be announced.
Fri. May 8	4pm. Project 2 due. No late projects allowed unless you talk to me more than one week before.
Wed. May 6	HW: Problems from Sections 5.5, 5.6, 5.7 DO NOT TURN IN. I will give solutions in class.	We will omit Section 5.4
Wed. April 29	HW: Problems from Sections 5.1, 5.2, 5.3
Wed. April 22	EXAM 2 Over sections we covered from Chapters 3 and 4. One side of 8.5 x 11" sheet of paper allowed for notes. No technology.
Wed. April 15	HW: Problems from Sections 4.6 and 4.7
Wed. April 8	HW: Problems from Sections 4.3, 4.4, and 4.5	There is an extra problem for Section 4.5 (see below).
Wed. April 1	HW: Problems from Sections 4.1 and 4.2
Wed. March 18	HW: Problems from Sections 3.6, 3.7, and 3.8
Wed. March 11	HW: Problems from Sections 3.2, 3.4, and 3.5
Wed. March 4	PROJECT 1 is Due. HW: Problems from Sections 3.1 and 3.3	Section 3.2 problems will be due next week.
Wed. Feb. 25	EXAM 1 Over sections we covered from Chapters 1 and 2. One side of 8.5 x 11" sheet of paper allowed for notes No technology.	No homework is due. Solutions to S2.10 will be given in class.
Wed. Feb. 18	HW: Problems from Sections 2.6, 2.7, 2.8 (don't forget world population problem).
Wed. Feb. 11	HW: Problems from Sections 2.3, 2.4, 2.5
Wed. Feb. 4	HW: Problems from Sections 1.3, 2.1, 2.2
Wed. Jan. 28	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 (listed below)