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 plus any time I am not otherwise occupied, and, if all
else fails, 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.

ASSIGNMENTS THAT ARE HANDED
IN MORE THAN A DAY LATE MAY INCUR A PENALTY.

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.

Assignments:

1)
Pg 17 # 1-6, 8,9

2)
pg 18 # 24 and 26

3)
pg 43 # 4, 13, 21, 25

4)
Exponential decay …page 43, # 35, 36; plus: some of the oldest rock on Earth is
found in Northern Canada; it’s said to be approximately 4 billion years old.
What percentage of ^{40}K would you expect to find in this rock?

Exponential
growth…page 43, # 34

5) Solve dT/dt = k( A – T) to obtain Newton’s
Law of cooling/heating: T = A – (A-T_{0})exp(-kt). Then do problem #43 on page 44 and problem #65 on page
45, as sketched out in class.

6)
pg 84 # 29 as discussed in class

7)
page 54 # 8, 9, 15, 18, 22

8)
Look at problems # 1through 8 on page 72. Take each one separately and reduce
until you can say whether it’s Bernoulli or not.

I = -8f it is, say what n is and what
substitution you would make. Then solve the last one you find.

9)
page 73 # 33-37 Check each of these to see if it
passes the test for exactness…yes or no. You don’t need to do anything after
that.

10)
A handout on exactness. Copies posted on my door if you missed class.

11)
page 94 # 25 parts a and b. We laid the groundwork for
this homework thoroughly in Friday’s class; there’s a chance for an egregious
error if you missed this lecture.

12)
(a) Using data from the handout sheet, figure out what
the escape velocity would be for : our SUN, the EARTH’S MOON and for MARS.

(b) To what radius must the SUN be shrunk to
create a black hole? ( This is pg
94, # 24 b in the text.) Same problem
for JUPITER.

So, all together, you have FIVE computational
problems.

( I’ll
put a couple of copies of the handout on my door just in case.)

13)
page 112 # 33-38, 41 and 42. Show what little
computation there is.

14)
straight drill problems…..pg
112 # 39,40 and page 134 # 4 -9 (show
how you get the characteristic roots in all cases)

15)
page 145 #1,2,3 ( in all problems just give the period
and frequency)

16)
pg 145 #4

17)
Find the solution in the form of a damped, shifted cosine:

a)
m =25, c = 10, k=226 ( roots are -1/5 __+__3i)

b)
m=2, c =12, k = 50 (
roots are -3 __+__ 4i )

18)
For each of these systems, find the particular solution as a damped shifted
cosine. Then draw a sketch of the solution curve as outlined in class.

a) m=25, c =10, k =
226 with x_{0} = 20, v_{0 }= 41

b) m = 2, c =12, k =
50 x_{0} = 0, v_{0} =
-8

19)
Given the system m =3, c = 30, k=63; for each of the following sets of
initial data, find the complete solution. Then
determine whether there is a positive overshoot and, if so, find t^{*}.
Finally, incorporate all this into a sketch of the graph.

a) x_{0}=2
, v_{0} = 2

b) x_{0}
= 2, v_{0} = 3

c) x_{0}
=2, v_{0}=0