Here are solutions (updated: June 5, 1:00PM) to the practice problems. These are predominantly just answers. On a few problems, I gave some more detail, and on some others, I gave some hints.
I also modified a few of the problems to be more reasonable, so here's an updated set of practice problems.
On Thursday, I need to move my office hours earlier in the day: all TAs are required to attend a departmental meeting that directly conflicts with our usual hours. In their place, I will have the following hours
I have created some practice final questions to help you prepare for the final next Wednesday. I need to write some solutions for some of the problems still, but these will be forthcoming.
I'm very pleased to present you with your final homework. This homework is due the last day of classes, Friday, June 1. Don't forget you have a quiz on Friday, May 25!
Update (5/29) You are not required to do 6.5.13b.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 6.4 | 9, 10 | 12, 18 |
| 6.5 | 4, 5, 13a |
Included with the homework this week are 3 problems not found within the book. They are found in the attached pdf. The homework is due next Wednesday, May 23.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 6.2 | 4, 10, 14 | 21, 22, 23 |
| 6.1 / 6.2 | Supplemental Problems |
I've written up solutions to both the practice exams. Take what you can from the second practice exam, but multiple questions are formula/calculator questions (especially 3c, 3d and 4). I'm pretty sure he has a typo on his first problem as well (in the initial conditions), but I've solved it out about as fully as one can hope.
As for my exam, the problems were definitely too easy, so keep that in mind as well. Somewhere in between in these two exams is a happy medium.
Here are some sample previous midterms for you to practice. From the first practice midterm, be sure you can do all the problems, as well as plot the steady state responses on problems 3 and 4 (up to phase). From the second practice test, you should try to do all the problems. Note that the second exam is likely too long for our class.
I'd like to congratulate everyone who tried the first set of bonus problems. There was a lot of really nice work, and I hope you consider trying the second set of bonus problems (even if you did not try the first). I am attaching a Maple document which outlines how I approached the first set. I hope you take a look at it!
I'm very pleased to present you with the second bonus problem set: approximating the nonlinear spring equation by the linear spring equation. These will be all the remaining bonus problems for the course. I'll have them due on the last day of the course, Friday, June 1st. You must do the first two problems to be eligible to receive credit on the second two problems.
Here are solutions for the correct form guesses on the worksheet. If you're looking for the correct coefficients – something that will not be tested on the quiz – I invite you take advantage of Maple to verify your solutions.
This is your homework for next week. The majority of the complexity of these problems lies in interpreting the text and interpreting the math you do -- the actual calculations you'll be doing are more-or-less the same as in 3.5 (and arguably simpler).
You'll need to switch between \( A \cos \omega_0 t + B \sin \omega_0 t \) and \( R \cos( \omega_0 t - \delta) \) multiple times in this homework. You've done this calculation once before, but the book has a good discussion on page 195 (using the numbers at the top of the page). Look at equations (12) through (17) especially. The text after equation (17) is important for the phase \(\delta\) as well.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 3.7 | 7, 11 | 6, 21 |
| 3.8 | 11, 17abd | 5, 10 |
Here is a worksheet to help you practice undetermined coefficients. This includes a brief write-up of the method, which you might find more to-the-point than the book.
New homework is up. It'll be due next Wednesday. The suggested problems from 3.4 will help if you're looking to practice solving homogeneous equations. Even though these problems appear in the repeated roots section, they include other types of characteristic polynomials as well.
The problems from 3.3 cover a famous special second order differential equation with non-constant coefficients. There aren't too many of these that can actually be solved, and there are even fewer whose solutions can be as efficiently described as these. I strongly encourage you try problem 34 while you're looking at this section, but you do not need to do it for your homework.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 3.3 | 35 | 34,36 |
| 3.4 | 1,3,5,7,12 | |
| 3.5 | 3,4,13,28 | 5,7,8 |
I put a bad, bad sign error in the bonus problem. It ruins everything. In the third problem, a plus sign should be a minus. I've corrected this formula in the new PDF.
In light of this, the bonus problem due date is extended to Monday. The only computer print-outs you need are the graphs. These may be printed directly. Please label your graphs (you may do this by hand). Any other text the problem requests may be written by hand.
Here are solutions to the practice midterm. I decided to provide fuller explanations, so if you're having trouble understanding one of the problems, be sure to take a look. Don't forget to practice Euler's method! You might want to use your notesheet to help remember this!
Here is the midterm from last year. Answers will be forthcoming. Bear in mind that our midterm will also cover Euler's method for approximating differential equations. I have listed some suggested problems from 2.7 for practice.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 2.7 | 1ab, 3ab |
Here is the sample problem I gave you in class today. I'll ask you about this and/or a simpler population model for the quiz on Monday!
Here is your third homework, due next Wednesday. We will have a quiz on Monday covering different population models and turning word problems into differential equations. The problems from 2.5 are a big help: pay especially close attention to whether or not you understand from where the differential equations in the book come. Problem 13 of Section 2.3 from last week's homework is another important example.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 2.4 | 22 | 7,8 |
| 2.5 | 16a, 17a, 18, 20 | 3,4,7 |
Here is your second homework, due next Wednesday. On Friday we will cover more of Section 2.3, and I will hopefully put more of you back at ease, after today's disquieting lecture. If you're bothered by the \(\log(1+r)\), continuous compounding, and the like, consider looking at Example 2 of 2.3 (page 54 and 55). The book is pretty good here, but I want everyone to be on guard about the interpretation of the \(r\) in \[ \frac{dS}{dt} = r \cdot S, \] something about which the book is not so great.
The bottom line is that I want you all to be able to build differential equations that do what you want them to do, and I think we'll get there one way or the other.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 2.1 | 13,16,20,28 | 1,2,3,18,19 |
| 2.3 | 13,18ac | 2,6,8,32 |
Here are the quiz solutions. I plan to have them graded by Monday. Have a great weekend!
The first homework assignment is due next Wednesday in class. Please remember to staple your homework.
Homework is essential to learning mathematics; arguably, the only way to learn math is to do it. That said, I've made the homework assignments relatively short, to allow you to spend time preparing for the class as you see fit. For this reason, I've supplied additional problems that provide you with extra practice if you desire to do them. These will not be graded, but I encourage you to discuss them with me in office hours.
| Section | Assigned Problems | Suggested Problems |
|---|---|---|
| 1.1 | Matching Worksheet | 15-20 |
| 1.3 | 17 | 14,19 |
| 2.2 | 13ac, 14ac, 22, 23 | 2,3,6,8 |
You do not need to print out the matching worksheet, but clearly label to what your answers refer.
I've created a solution sheet for the integral practice problems. Always question the math you read that is stated as fact. Lots of it is wrong, even when it comes from a trusted source. That said, I've checked these twice.
Hello and Welcome to the class webpage for Math 307 B. All class resources, including homework assignments, will be posted on this page as we progress. While you're here, be sure to glance at the syllabus, the preliminary calendar, and the short Maple introduction.
On the first Friday of class, we will have a quiz to review integration techniques. To help you brush up on these techniques, I've created some practice problems. You'll be using lots of integration all quarter long, and you can set yourself up really well to succeed by making sure you remember the various techniques!
| Office | Padelford C-8K |
|---|---|
| paquette//math.washington.edu | |
| Office Hours | Thu 4:30-5:30, and Mon 10:30-11:30 |
| Lecture | MWF 9:30 - 10:20 in LOW 205 |
|---|---|
| Midterms | Mon, Apr 23rd and Mon, May 14th |
| Final | Wed June 6 in LOW 205, 8:30-10:20 |