MATH 331

MATH 331 : DIFFERENTIAL EQUATIONS : SECTION 2 : SPRING 2007

Instructor: Mike Diehl

Office: LGRT 1323H

Lecture: Tuesday/Thursday: 9:30-10:45 in LGRC A205

Office Hours: Tuesday/Wednesday: 1:30-2:30 in LGRT 1323H

ANNOUNCEMENTS

CLASS NOTES

SEMESTER PROJECT - DUE FRIDAY, MAY 11

HOMEWORK ASSIGNMENTS AND QUIZZES

HW #1 - Due Thursday, February 8

1.1: 2, 4
1.2: 7, 15, 16
2.2: 7, 13ac
HINT: 15b is poorly worded...they want you to find the time when the temperature of the object is u₀ - .5(u₀ - T), since this represents the initial temperature that has been reduced by half of the initial temperature difference between the object and the room.
SOLUTIONS

QUIZ A - In class on Tuesday, February 13

Review of calculus: Properties of the natural log and exponential functions, integration by parts, partial derivatives

HW#2 - Due Thursday, February 15

2.1: 2c, 11c, 15, 17
2.2: 31, 32
2.5: 9, 22 : For #9, just draw the slope field, find the constant solutions, classify their stability and draw some integral curves
SOLUTIONS

HW #3 - Due Friday, February 23

2.3: 4, 19, 21, 23
For #19c, just do lakes Superior and Erie. The V in the chart is in 1000's, so you should use V=12,200 and V=4600
#21 we did in class, so you should just use what we did to answer the questions. Do the graphs in part c, but don't do the comparison.
For #23, use g = 32, and m = 5.625. You should set it up as a two-part problem, one for before the chute is open, and one for after. The initial values for the second part are the end values of the first part. In part c, they want you to take the limit of v(t) as t goes to infinity.
We don't have class, so there's no quiz and everyone should turn in written homework by putting it in the envelope on my office door by Friday afternoon. I should be around on Friday if people want to stop by with questions.
SOLUTIONS

HW #4 - Due Thursday, March 1

2.6: 4, 10, 26, 28: For #26 try an integrating factor u(x), and for #28 try an integrating factor u(y)
SOLUTIONS

MIDTERM EXAM #1 - Monday, March 12 at 6:00 in LGRC A205

Covers all of the material that we did from Chapter 2, but will not include anything from Chapter 3
You should bring a pencil/pen, but NO CALCULATORS are needed
Here are some review problems from the textbook
- Page 131: 1, 6, 10, 14, 20, 21
- Section 2.3: 1, 22
- Section 2.5: 12
Here is a practice exam from a few years ago
SOLUTIONS TO MIDTERM #1

HW #5 - Due Thursday, March 15

HW #6 - Due Tuesday, April 3

3.6: 2, 5, 7 (find the general solutions) 3, 17 (just tell me what the correct guess would be, but DON'T actually find the solutions)
3.7: 7, 13
SOLUTIONS
I had a couple of sign errors in my solutions to the problems from 3.7, so please check those problems' solutions HERE

HW# 7 - Due Thursday, April 12

3.8: 10, 28ab - For #10, the gravitational constant is g = 32
3.9: 6, 8abc
Using the same setup as 3.8 #10, suppose that now instead of it being homogeneous, you will throw an object of weight W on top of the mass that's already hanging, at rest, on the spring. This sets the spring into motion from equilibrium with an initial velocity of 0.25 ft/sec. It's also true that when the spring is at equilibrium, the mass is only 0.2 feet off the ground
- Write down a solve the DE for the position of the mass at time t. Check the spring notes for help in setting this one up. Use the initial conditions to find c₁ and c₂, in terms of W.
- Using your calculator, graph the solutions for 3 different weights: W = 10 lbs, 5 lbs, 0.3 lbs
- Looking at your graphs, for each W-value, answer the following questions and indicate where (if anywhere) these events occur on each graph:
  - Does the mass ever hit the ground?
  - Does the mass ever return to its original (equilibrium) position?
  - What is happening to the position as t goes to infinity?
  - Discuss the differences in the graphs of the 3 different W-values, and compare them with your graph from #10, which is for W = 0.
Do your best with this last problem...I know it's a bit tough, but it's similar to the problems you'll see in the project.
SOLUTIONS

IN-CLASS EXTRA CREDIT SPRING PROJECT

MIDTERM EXAM #2 - Monday, April 23 at 6:00pm in LGRC A205

This exam covers all of the material that we did from chapter 3. It does NOT include Laplace transforms
You should bring a pen/pencil, but NO CALCULATORS are permitted on this exam
Here's the CHEAT SHEET that I will give you on the exam
Here are some review problems:
- 3.1: 10
- 3.4: 11
- 3.5: 6, 26
- 3.6: 8, 16
- 3.7: 6, 15
- 3.8: 11 - just setup and solve the system
- 3.9: 5, 7ab
Here's a practice exam from a few years ago
On the exam, I will make the math computations easy, and I'll be sure to give you the value of the appropriate gravitational constant. Also, you won't have to worry about converting units, or drawing graphs.
Just a reminder/warning: Calculus and algebra mistakes were abundant in the first exam, so please review your skills and take your time during the exam.
SOLUTIONS TO MIDTERM #2

HW #8 - Due Friday, April 27

QUIZ B - Tuesday May 1

HW #9 - Due Thursday, May 3

HW #10 - Due Thursday, May 10

PROJECT - Due Friday, May 11th - CLICK HERE FOR DETAILS

FINAL EXAM - Friday, May 18th at 10:30 in LGRC A301

The final exam will be CUMULATIVE, and will contain problems from the three chapters we covered: 2, 3 and 6.
There will be NO WORD PROBLEMS on this exam. Nor will there be any first order equations which require the homogenous or exact methods.
I will provide a CHEAT SHEET, as well as the Laplace transform chart that we've been using.
As usual, no calculators are permitted on this exam, as the arithmetic and calculus should be relatively easy.
Here are some practice problems for Chapter 6:
- 6.2: 9, 21
- 6.3: 15, 17
- 6.4: 1, 9
- 6.5: 1, 5
- 6.6: 10
SOLUTIONS TO FINAL EXAM