Homework assignments

These assignments are subject to change. I suggest that you not bother to print this page.

Assignment 1.1--1.4, due Thursday, August 31

Long before the due date, read pages 1-5, 6-13, 15-19, and 23-27.
(In Section 1.3, you can stop on page 19 before "The Method of Isoclines".)

Section 1.1
Browse problems 1-12 (except 3 and 11) to make sure you're clear on the concepts of "order," "independent variable" and "dependent variable." Do you recognize any of these equations (or their descriptions) from your own field of study? (You may not need to write anything down about problems 1-12.)
Do Problems 15, 16.

Section 1.2
Problems 6, 7, 10, 14, 18, 20, 21, 24, 27, 28.
For Problem 9: An "implicit solution" is defined in Section 1.2. Do you remember "implicit differentiation?" Sometimes you can only solve an ODE implicitly. This is still considered an analytic solution, and for practical purposes is probably just as good as an explicit solution.

Section 1.3
Problems 1-4, 10, 18.
Directions for Problem 10: Sketch, the direction fields by hand. OK, this is tedious. Try for a reasonably detailed sketch of the direction field for ODE (a) and sketch some solutions. Then if you feel comfortable with the method, spend your time doing something else. But make sure you're comfortable, for example, with the following kind of question: draw a slope line (one of the little hash marks making up the direction field) at (2,-4) for the ODE y' = (1- x) y².
Directions for Problem 18: Either sketch the direction field in detail or (cooler) think about what the direction field looks like and answer the question posed.

Section 1.4
Problems 5 and 6.

Assignment 2.1--2.4, due Thursday, September 7

Long before the due date, read pages 38-40, 41-45, 48-54, and 57-63.

Section 2.2
Problems 1-6, 8, 9, 15, 23, 26, 30.
For Problems 1-6, Read the directions!
Section 2.3
Problems 1-6, 7-10, 13, 14, 17, 23, 24, 28, 29.
For Problems 1-6, Read the directions!
Additional hint for 29: If you choose to think of x as a function of y instead of y as a function of x, how do you determine dx/dy in terms of dy/dx? Think about slopes.
Section 2.4
Problems 1-8, 10, 11, 15, 17, 32, 33.
For Problems 1-8, Read the directions! I am also adding additional directions: For each of these, write the ODE in "standard" form, i.e. with derivatives dy/dx rather than "differentials" dx and dy.

Assignment 3.2, 4.1-4.2, due Thursday, September 14

Long before the due date, read pages 90-92, 92-95, 152-156, and 157-163.
(In Section 3.2, you can stop before Population Models. You may be interested in the rest of Section 3.2, i.e. pages 95-100, and maybe more of Chapter 3, but there is no homework on it.)

Section 3.2
Problems 1, 3, 5.
Section 4.2
Problems 2, 3, 9, 12, 16, 17, 19, 26, 35, 37, 38.
Comment on 37 and 38: To solve an nth order linear ODE, you need to find n linearly independent solutions. BUT, as we discussed in class, the definition of linear independence is more complicated for n greater than 2. (See Problem 35 for a review of the definition we discussed in class.) However, if your ODE has constant coefficients, you can use the "auxiliary equation" method, just like for 2nd order ODEs and find three solutions. These solutions will be linearly independent and you don't need to check that when you do these problems.

Assignment 4.3-4.4, due Thursday, September 21

Long before the due date, read pages 165-172 and 174-180.

Section 4.3
Problems 2, 6, 8, 12, 16, 17, 20, 21, 26.
Section 4.4
Problems 1, 3, 4, 10, 12, 14, 15, 17, 21, 26, 29, 30, 33.

Assignment 4.5, due Thursday, September 28

Long before the due date, read pages 180-185.
(You may be interested in Section 4.6, pages 187-191, but there is no homework on it.)

Section 4.5
Problems 2, 3, 5, 7, 18-21, 31-36.

Assignment 4.9-4.10 due Thursday, October 5

Long before the due date, read pages 212-220 and 221-227.

Section 4.9
Problems 1, 4, 9.
Additional directions for Problems 1, 4, 9: Also write the solution in the form A sin (omega t + phi) or in the form A e^atsin (omega t + phi)
Section 4.10
1-5, 9, 11

Assignment 7.1-7.2, due Thursday, October 12

Long before the due date, read pages 350-352 and 353-360.

Section 7.2
Problems 1, 4, 5, 6, 9, 10, 12, 13-30.
For Problems 21-28: Do as much sketching as you think is helpful for you, but this is certainly something you should be able to do.

Assignment 7.3, due Thursday, October 19

Long before the due date, read pages 361-365.

Section 7.3
Problems 1-11, 21-25.
For Problem 22: Don't worry about "using induction". Just see that the pattern they describe seems to work.

Assignment 7.4-7.5, due Thursday, October 26

Long before the due date, read pages 366-374 and 376-382.

Section 7.4
Problems 2, 3, 5, 8, 13, 17, 20, 21, 25, 33-37.

Section 7.5
Problems 1, 2, 3, 5, 12, 14, 20, 21, 23, 24, 25, 27, 29, 35, 37. In problems 20 and 21, don't stop where the book directions tell you to stop. Finish the problem and solve the original IVP.

Assignment 7.6--7.9, due Thursday, November 2

Long before the due date, read pages 383-389, 392-393, 397-403, and 405-410.
(In Section 7.7, you can stop on page 393 before Example 2 if you want to, although the remaining material is very interesting.)

Section 7.6
Problems 1, 3, 6, 11, 13, 21, 22.

Section 7.7
Problems 1-4.

Section 7.8
Problems 1, 3, 5-14, 31, 32, 35.
Problem 35 is asking you to see why "Transforms of integrals" is just a specific case of convolution.

Section 7.9
Problems 1-12, 21-22, 29-30.
Problems 1 to 12: These will become very easy once you understand them, so ask someone for help if you are stuck for too long.
Hint for 9 through 12: Use the definition of Laplace transform and Equation (3) on page 407.

Assignment 9.1-9.3, due Thursday, November 9

Long before the due date, read pages 496-499, 500-503, and 504-513.
To the extent that any material is Sections 9.2-9.3 is review for you, use your own judgement about how much time to put into it. But make sure you really know it. The last 9 problems assigned from 9.3 are particularly important.

Section 9.1
Problems 1-5, 7-10.

Section 9.2
Problems 3, 4, 5, 6, 11, 12.

Section 9.3
Problems 1, 3, 8, 9, 21-29.

Assignment 9.4-9.5, due Thursday, November 16

Long before the due date, read pages 515-520 and 523-530.

Section 9.4
Problems 1, 3, 4, 9, 10, 12.

Section 9.5
Problems 1-16, 31-34.

Assignment 9.6, 5.4, "due" Thursday, November 23.

Long before the due date, read pages 534-537 and 262-270.

Section 9.6
Problems 1-4, 13, 14.

Section 5.4
Problems 1-9, 11, 12.

Assignment 12.1-12.3, due Thursday, November 30.

Section 12.2
Problems 1, 3, 4, 6, 13, 15, 16, 18, 19, 20.
Problems 13-20: Sketch by hand.

Section 12.3
Problems 1-6, 17, 19.
Problems 17 and 19: Sketch by hand.