MAT 311 Ordinary Differential Equations ( 32212)

MWF 9:20-10:15 ES 147

Instructor: Professor Edward Thomas ES 132F phone 442-4623

By far the best way to contact me is: et392@albany.edu

Text: Elementary Differential Equations ( 6^th Ed) by Edwards and Penney

This is a pretty big class so let’s establish some GROUND RULES at the outset.

Ø NO cell phones or other such devices will be used during the class. TURN THEM OFF.

Ø Please organize your schedule so that you are in your seat ready to rock and roll at the stroke of 9:20. The instructor is an old man and is easily irritated by peeps coming in late. WE DON’T WANT THAT.

Ø And finally, classes begin on Monday, August 31^st. THIS IS NOT OPTIONAL.

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Chapters 1 through 4 constitute the core of the course. We will cover most of each Chapter. The emphasis will be on solution techniques and important applications of differential equations.

If there was ever a course where you can learn the material by doing problems, this is it. So here is how it’s going to work.

I will assign problems every day. You will hand in these problem sets at the next class. I’ll correct them and get them back to you right away. These assignments will count ONE THIRD of your final grade.

There will be two exams which will make up the rest of the grade. Each exam will cover approximately one half of the semester’s material.

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.ASSIGNMENTS

1) pages 8 and 9 # 5,6,7, 15, 16, 18, 19, 22

2) pg 17 # 2, 3, 6 and pg 18 # 42

3) pg 43 # 3, 4, 12, 13, 20, 21, 25 Be careful, both with your calculus computations and with your algebra.

4) pg 43 # 35, 36

Homework Policy. If you need to tweak your homework then hand it in later that day or the next morning. After that it is regarded as late homework. It may be graded with a penalty or ...if it’s real late...not at all.

5) pg 44 #40, 43, and 49

6) pg 54 # 2, 5, 24 plus a first order linear equation assigned and discussed in class

7) (a) In the insulated tool shed problem, with k=.2 and omega equal to Pi/12, show that the indoor temperature variation is about 60% of the outdoor variation, a.

(b) What if k=.4? k = .1?

8) pg 73 # 32-35

9) Finish the problem begun in class and also do # 21 pg 83 Added on Tuesday...thanks to Luigi for pointing out that in problem 21, the units of population are millions. So the max population is 200 million and the initial value is 100 million.

10) page 83 # 24 and page 84 # 32

11) page 134 # 1-4 and # 21. On numbers 1 through 4. add the following initial data: y(0)=1, y’(0)=2. The other problem already has initial data

12) page 134 # 5, 6, 7, 8 with initial data y(0) =1, y’(0) = 2 plus problem # 22. Comments: Problems 5, 7, and 8 are the easiest. In number 8, you should get c1=1 and c2=-1/2. Problem 6 is hard because the roots themselves are messy. Even if you can’t finish it, at the very least get the book answer for the general solution. Problem 22 involves a couple of little computational issues. One of them is that the square root of -108 works out to 6 times sqrt(3)i. Another is that sqrt(3)/3 = 1/sqrt(3). With that in mind you can get the book answer.

13) pg 145 # 1, 2 , 3, 4

14) pg 147 # 13 and 14a

15) page 161 # 1, 2, 3, 4 and 6

16) A problem assigned in class plus page 161 # 31, 32, 33

17) pg 161 # 21 plus two in-class problems on duplication and page 171 #1, 2

18)Two problems on resonance. The first problem is to finish the computation of the particular solution in the case where w0 is not equal to w. Obtain the values of A and B that were given in class. The second problem is # 6 on page 171....this is the case where w0 = w...pure resonance.

19) pg 171 Do # 11 and 12 as follows...calculate the steady state solution and steady state amplitude. Find the form of the transient solution. You do not need to calculate the coefficients in the transient solution, so you can ignore the initial data. Do not bother with graphs.

20) page 275 # 1, 3, 4

21) page 287 # 3, 4

22) page 287 # 5, 6 Saturday morning...For problem 6, the correct form of the partial fraction decomposition is

As/(s^2+1) + Bs/(s^2 +4). Note the s in each numerator.

23) page 275 # 7,8,9,10 Each problem should be done as discussed in class, using shifted u-functions and the table of transforms in the front of the book. Plus page 314 # 1,2,5,7.

On problem 10, the function that is being truncated is f(t) = 1-t. That makes things easier than problem 9. In problem 9, you had u(t-1) times t and to transform that you need to rewrite it as u(t-1)((t-1)+1) and distribute the u(t-1) through.

24) page 315 # 32, 33

25) page 206 # 1, 2 Remark Tuesday morning: On both these problems, you need to rewrite the equation with all the y terms on the LHS and zero on the RHS, like we did in class.

26) Finish the problems that we started in class. The first one was to solve y’ + 2xy =0. And for the equation y” + y =0, solve recursively for all even coefficients in terms of c0 and odds in terms of c1.

27) page 206 # 12, 13 ( see if you can identify the solutions as familiar functions) and page 206 # 22( the first four or five terms at least) Saturday AM....In # 12, 13 the solutions are indeed familiar, but there are a couple of tricks involved. I’ll show you on Monday. And, on #22, it’s OK to just write out the first few terms and stop. If you want to verify that the solution is e^(-2x), then it helps NOT to cancel anything when you are computing the numerical values of the c’s.

28) Compute the Legendre coefficients c5 and c6 in terms of c1 and c0, resp., and present them with the numerators factored as we did in class. Then, write out the Legendre polynomials corresponding to alpha = 3, -3, and 4. Tuesday AM Just as a check, your answer for alpha = -3, should come out to 1 + 3 (x^2)

29) Solve for the first four or five terms of the series for the Bessel functions of order 0 and 1, as discussed in class.

30) Solve the equation z” +z =k/h^2 as discussed in class and show that 1/z can be written in form (12) on page 338. This will set up Kepler’s second law of motion.