fAMAT311  Ordinary Differential Equations

MWF 9:20-10:15  ES 147

 

Instructor: Professor Edward Thomas  ES 132F

Phone 442-4623

Best way to reach me is by email: et392@albany.edu

Office hours: MWF 10:25-10:45, 12:50-1:30, 2:45-3:15 and by appointment

A link to the class webpage will be found at : www.albany.edu/~et392/AMAT311.htm

 

Text: Elementary Differential Equations by Edward and Penney; we will be covering Chapters 1 through 4, plus other topics if time permits.

 

   You need to have this text on the first day of class, not at some indeterminate later date (see the next paragraph.) If you show up on the first day of class without the text, I will take this as a sign of LACK OF PREPARATION.

 

  In this course, you can learn both technique and theory by doing problems. So I am going to assign problems every single day, starting on day one. They will be collected, graded and returned to you at the next meeting and will serve as the springboard for what comes next. You should assign them high priority…I’m not kidding on this.

 

  Daily assignments will count one third of the grade. The other two thirds will come from a Midterm and a Final.

 

 

   Let’s articulate  some ground rules:

 

> First...there will be ABSOLUTELY NO CELL PHONES, LAPTOPS or any other type of electronic devices in use during class. Please take care of business and TURN THEM OFF before you enter the classroom.

 

>Second…please DO NOT come to class late as it is disruptive. Be in your seat, mentally alert and ready to participate, at 9:20 when class begins.

 

> Third  …If you get sick or have some other kind of emergency, please get in touch with me as soon as you can so we can work things out.

 

 > Fourth, classes begin on Monday, August 25th. ( You wouldn’t believe it but in the past some peeps thought they could begin classes on a day of their own choosing. That was a BIG mistake.)

 

Assignments:

1)   page 17 # 1-6 and 8,9  ( Geez! Already?  Ashley has pointed out that there is a mistake in the answer section for this assignment !)

2) page 18 # 24, 26 and 36 plus page 43 # 1-4  Some remarks:   On problem 26, tMAX is approximately20.4 seconds.

On problem 36, you are given that xMAX = 2.25, from which you want to compute v0. First compute tMAX. You’ll find that tMAX =v0 / gE ( Earth’s gravitational constant) Then using that, you find that xMAX =v02 /2gE. and from that you can figure out  v0.

3) page 43 # 21, 22, 25

 4) Using the value of k that we found in class, predict the U.S. population in 1920 ( compare with the actual value of about 106 million) Plus, on page 43, do numbers 33-38

 5) page 84 #32 ( just do the derivation as discussed in class…i.e., go from equation (*) to this form of the solution) and # 29 ( on part c , maybe just see how accurately the Verhulst model predicts P(2000)or P(1990)

 6) page 44-45 # 43, 48, 65

7) page 54 # 2, 3, 4, 8, 15, 17, 22, and 24

8) page 55 # 33, 35

 9) A handout on exactness. I’ll post a couple of extra copies on my door.

10) pg 73 # 33, 35, 37, 39 Do these by the systematic way introduced in class, please.

11) Using the numbers provided in class ( copies on my door) compute escape velocity for the Sun, Earth, Moon and Antares. Then, for the Sun, Moon and Antares,  compute what radius will produce a black hole…as we did in class for the Earth.

12) pg 111 # 1, 2, 5, 6

13) A handout with 8 problems on solving second order equations..copies on my door ( The equation in problem 4 should end in 25y, not just 25. Sorry for the misprint.) Comments added Saturday morning….if you have complex roots a+bi and a-bi and the a is equal to 0, the corresponding real solutions are just cos(bx) and sin(bx), since eax=1. Also, in the first problem, the roots are real; they are approximately -3.62 and -1.38.

14) Solve the spring/mass equations with the following data: (1) m =4  k= 16  x(0)= 2  x’(0) = -3 and (2) m = 1  k= 9  x(0) = -1  x’(0) =0

15) page145 #1-4

 

    Announcement about late homework….I’m afraid I have been encouraging bad habits among a very few of us. From now on, unless you have spoken with me in advance, as soon as I start grading an assignment any previous assignments that have not been handed in will be regarded as late. They may incur a late penalty or, if they’re REALLY late, they may not get graded at all.

 

16) page 147 # 13 a, # 15,16  In each case simply find the solution  using initial data, and, in #13, find the time to reach max displacement: tmax =?

17) page 147 # 18 and 20

18) page 161 # 1, 2, 3

 I also passed out a list of topics from which exam questions will be selected. I’ll post copies on my door.

               

  MIDTERM  Monday  October 13 th

19) page 161 # 31, 32, 3320)  Calculate the response amplitude for the system x” + 16x = sin ( omega)t when omega = 4.1, 4.08, 4.05 , respectively. Suppose the system will collapse if the response amplitude reaches 5 units. What omega will produce this?   Then, let’s do an experiment. Suppose we look at x” + 9x = cos 3t. Show that the method of undetermined coefficients fails if we try a trial solution of the form xT = A cos 3t. ( We’ll see what to do about this next time.)

 

20) #1) for the equation x” + 9x = cos3t, substitute the trial solution xT = t (A cos3t + Bsin3t) and, after much computation, verify that the particular solution is            xp =(1/6) ( t sin3t)  #2) Then, using the initial data x(0) =1 and x’(0) = 5, find the complementary solution xc = sqrt (34)/3 cos ( 3t – phi).

The point here is to illustrate the dominance of xp when you have pure resonance.  #3) This problem gets us started on resonance in damped systems. Take the equation mx” + cx’ +kx = F0cos (omega)t. We want to work out the general form of the steady state solution, xp, so substitute the trial solution, xt = A cos ( omega)t + B sin(omega)t and calculate what A and B are in terms of K,m,omega, c and F0. We’ll go from there next time.