Math 33B, Differential Equations

Section 3, Winter 2008

Homework 10 - Due 3/14 (Assigned 3/7): Due at 5pm (slide under my office door): 9.6: 6, 7, 9, 14, 18, 19, 26, 27
9.8: 4-6, 10, 14, 16, 22, 24, 28, 30, 36, 38
This assignment will be graded out of 30 points, but there are a maximum of 40 points possible (to account for the fact it is a little longer than previous HWs). Any score over 30 will be extra credit and can go towards bumping up other HW scores.

Homework 9 - Due 3/7 (Assigned 2/29): (Solutions posted by the Reader can be found here): 9.3: 10-12, 14, 16, 18, 20, 22
9.5: 4, 9, 10, 15, 16, 22, 28, 33, 34

Homework 8 - Due 2/29 (Assigned 2/22): (Solutions posted by the Reader can be found here): 9.2: 4-6, 12, 18, 20, 24, 30, 32, 38, 58 (parts a and b only)
9.3*: 10-12, 14 (*This Part of the assignment will NOT be due this week. Instead, it will be part of HW 9 due 3/7)

Homework 7 - Due 2/22 (Assigned 2/15):(Solutions posted by the Reader can be found here): 8.4: 27, 28
8.5: 4, 6, 8, 9 12, 17, 20, 22, 24, 26, Two Problems Below
9.1: 2-4, 10, 18-20

Extra Problem 1: In class we wrote down Theorem 8.5.1: If x and y are two solutions to a linear, homogeneous system of differential equations, then any linear combination of them is. We showed in class that the theorem held for a specific example (as it should). Show that the theorem will work for any example (in other words, prove the theorem).

Extra Problem 2: In class we showed how to reduce any high-order differential equation into a system of first-order differential equations. Show that:
i) If we start with a high-order linear differential equation, then the resulting system of differential equations will also be linear.
ii) If we start with a high-order linear, homogeneous differential equation, then the resulting system of differential equations will also be homogeneous.

Homework 6 - Due 2/15 (Assigned 2/8):(Solutions posted by the Reader can be found here): 4.5: 24, 26, 34, 40, 43
4.6: 7, 8, 12, 14
4.7: Problem Below, 10, 16, 18
8.4: 2, 4, 7, 8, 11, 12, 26

Additional Problem for 4.7:
In class, we considered a forced, damped harmonic motion problem:

We showed that a particular complex solution had form:
where
I claimed that the real part of this was also a solution:
where
i) Verify that y(t) = Re(z(t))
ii) Verify that y(t) is indeed a particular solution by plugging it into the given differential equation.

Homework 5 - Due 2/8 (Assigned 2/1):(Solutions posted by the Reader can be found here): 4.3: 4, 6, 12, 16, 22, 24
4.4: 12, 16
4.5: 2, 6, 10, 11, 14, 18, 20

Homework 4 - Due 2/1 (Assigned 1/25): (Solutions posted by the Reader can be found here): 2.9: 12, 15, 16, 18, 20, 24 (For problems 16, 18, and 20, do only part iii of the problem)
4.1: 2, 5, 13, 14 ,18, 22, 26-28

Homework 3 - Due 1/25 (Assigned 1/18): (Solutions posted by the Reader can be found here): 2.6: 21-23, 26, 28, 36-38
2.7: 3, 4, 8 (Hint), 10, 26, 28

Homework 2 - Due 1/18 (Assigned 1/11): (Solutions posted by the Reader can be found here): 2.4: 2-4, 13, 18, 29, 32
2.5: 1, 2, 6* (There is a typo for this problem, see the announcement page here for a correction to this typo)
2.6: 2, 3, 10-12

Homework 1 - Due 1/11 (Assigned 1/07): (Solutions posted by the Reader can be found here): 2.1: 3, 4-7, 12-14, 18, 19, 22 (draw the direction field by hand as in 18 and 19 if you don't have access to a plotting program)
2.2: 3, 6, 8, 10, 14, 33 (Hint)