AMAT311  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 techniques 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 Wednesday January 22nd. ( 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 # 1,2,3,6,8,9,and 11,12

2)  First, in the problem we analyzed in class, with initial velocity 50 and initial height 100, what is the impact velocity, vTHUD ? Next,  on page 18, let’s do # 24,26 and 31.

3)  Page 43 # 4,13, 21, 22,25

4)   Page 43 # 33-37

5)  Both problems have to do with the logistic equation which we began discussing in class. First, expand 1/P(150-P) by partial fractions and integrate. Second, after integrating, show that P/(150 – P) = C e (.06)t  We’ll pick it up there next time.

6)    Using the values of k and M postulated in the Verhulst model, predict the US population values for the years 1845 and 1895. ( These are remarkably accurate.)     Next, in the Doomsday/Extinction model which we started in class, show that if P0 = 200 then Doomsday will occur sometime in the 23rd year.

7)   Page 54 # 1-4, 17, 18, 24. Put each of these in linear form and calculate the integrating factor. You can stop there. Make two copies…one to hand in and one to keep/

8)  Page 54 Finish #1-4, 18 and 24

9)  A handout sheet on a linear equation which arises in connection with a falling body encountering air resistance. YOU KINDA HAD TO BE THERE.

10)        A handout on exact equations

11)        page98 # 2 -12 . As discussed in class, just test each equation to determine if it is separable, linear or exact (or none of the above) and stop there…you don’t need to solve.

The Midterm Exam will be on Monday, March 10th 

12) page 112 # 33-38

13) On page 134, take problems 3 – 9. Figure out which of them has complex roots and, for these, write out the general solution.

14) page 145 # 1 and 2

15) page 145 # 3 and 4

16) page 147 # 14 part (a)

17) page 161 # 1, 2, 3

18) page 161 # 31, 32, 33

19) A handout sheet with a problem on forced oscillations and resonance.

20) page 171 # 11, 12 ( omit finding c1 and c2 )

  21) First verify formula (21) on page 168 for the equations in problems 11 and 12 on page 171 (which we just did for homework.) ( Your answers for C should be  sqrt(10)/4 and 5/3 sqrt(29), resp.) Then, do # 17 and 18 on page 171 except don’t bother to graph C as a function of omega

22) A handout asking you to take the formula for response amplitude in a mechanical system and convert it to the corresponding formula for an electrical system. I will leave some copies of the handout on my door. Added on Tuesday morning….  it seemed to work out better for me if I took equation (2) , multiplied top and bottom by omega (w), then took the w in the denominator into the square root sign, did some algebra and THEN replaced L by m, R by c, 1/C by k and wE0 by F0 to get the form (1).

23) Compute the Laplace transforms of :   sin(5t),  e3t, and cos(t)…do these as improper integrals with limits and everything as shown in class. ( Who knows? This may be our last chance to do things this way.)

 

     24)(a) Compute L(t) as an improper integral. (b) Finish off the computation of L(u(t-a))  (c) Let g(t) = 1 – u(t-a). Compute L(g(t)) using known transforms and linearity. (d) Let h(t) = 12[ u(t-10) – u(t-30)]. Draw the graph of h(t) and tell what it might represent physically. Then, using linearity and known transforms, compute L ( h(t))

 

  25) Solve the following using Laplace transforms: (1) x’ -4x = 1 , x(0) arbitrary ; (2) x’ + x = e^(2t) , x(0) arbitrary; and    (3) x’ -5x = sint(t)  , x(0) arbitrary

 

26) page 287 # 1, 2, and 9

27) a) Derive the formula for the Laplace transform of a second derivative, using the formula for the first derivative. b) Following the idea in class, derive the formula for L(t3), L(t4) and then extrapolate to  get L(tn)

 

28) page 314 # 1, 2, 3 , 6, 7, 10

29) Try the bracket method to plot the solution to a problem you just did: #10 on page 314

 

30) page 324 #2