AMAT 314

MWF 1:40-2:35 ES 146

Instructor: Professor Edward
Thomas ES 132F

Phone 442-4623

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

Office hours: TBA

A link to the class webpage
will be found at : www.albany.edu/~et392/AMAT314.htm

Text: Mathematical Methods in
the Physical Sciences by Mary Boas. You
need to have this text on the first day of class, not at some indeterminate
later date. If you don’t have the text, I will take this as a sign of LACK OF
PREPARATION.

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 1:40 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
26th ( 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.)

The syllabus for this course
was developed in conjunction with the Physics Department about 10 years ago.
The emphasis is on those aspects of Mathematics that are can be readily applied
to problems in Physics. Chapters 6,7,8 and 9 of Boas ( the text) constitute the core of this
first semester of the course. So we will start in Chapter 6, Vector Analysis.
If you want to get a jump start, you might want to review relevant topics from Calc III such as the algebra of vectors, dot and cross products
and their geometric interpretation.
These topics are also covered quite well in Chapter 3 of Boas.

I’m going to assign problem sets EVERY DAY.
You will hand these in at the next class and I will grade them and get them
back to you pronto. The problem sets will count ONE THIRD of your final grade.
There will also be two exams, each covering about half the course. These will
make up the other two thirds of your grade.

Just for the record…when I say the assignments will count one third of
your grade, I’m not kidding. As I said above, doing problems is how you learn
the material

and how you prepare for the next class
and, besides that, there are some problems that require too much time to assign
on an exam. As a corollary to this, I cannot be grading batches of old
homework…please get the work to me on time.
And, to repeat the third ground rule….if you are sick or have an emergency, get
in touch with me so we can work things out.

OK ..let’s have
good semester!!

…………………………………………..

Assignments:

1) Page 105 # 12, 13, 15, 20 and 21

2) Page 284 # 7 and 9

3) Page 289 #2 a,
b and 4 and #5

4) Page 294 # 1-5

5) Page 295 # 11 and 14
Saturday am : In both problems, please make
nice BIG CLEAR pictures ( maybe a whole page) of the family of level curves. In
problem 11, use a contrasting color for the orthogonal trajectories ( the lines of heat flow). Also, in problem 14, draw in what
you think the orthogonal trajectories look like.

6) Page 306 # 1 a, b and #2a,b

7) Page 307 # 8, 9, 10

8) Page 307 # 11 and 14 and page 313, 314 #2 and 3

9) Page 314 #7 and 10 plus compute the divergence of the
field **F **= x i+
y j + z k/ ( x^{2 }+y^{2 }z^{2 )}

10)
Page 322 Hand
in # 1 plus try to set up #2-5 which I
will assign next time

11)
Page 322-323 # 2,
3, 4, 5, and 7, as discussed *ad nauseum *in class. Remember the misprint in #5, and in
number 7, try to use the
volume integral option.

12)
Page 334 # 3, 4,
7

13)
a) draw nice neat graphs of y = 2 sin(3x) and
y = -4 cos(5x) on the interval –Pi < x < Pi( I
hope I got those numbers right from class)

and b)
page 343 # 1-5( just the amplitude, period and frequency)

14)
Page 354 #1 and 2

EXAM I will be on Wednesday, Oct 16th

15)
(a)An object is
thrown upward with a speed of 20 ft./sec from a tower
60 feet high. Where is it after 1 sec? After 3 sec? When does it reach max
height? (b) same problem, only on the moon. ( c) Carbon 14 decays according to the classic equation
discussed in class. What fraction of the original amount is left after 2000
years? After 4000 years? How long do you have to wait until N(t)
= N_{0} /2?

16)
Page 398 #7 page
399 # 19 and page 400 #27,28 Here’s what you should do
on number 27. First, from the set-up I gave you in class, you should DERIVE the formula
T(t) = T_{A }+ ( T_{0 }– T_{A }) e ^{- k t} .
Then solve for k using the fact that when t = 10, T = 100^{o}. You will
find that k is approximately.15. Now you can do anything. That formula also
applies in problem 28, of course.

17)
Page 403 # 1-4

18)Finish
the problem we started in class plus do page 406 # 1, 2 and 3

19) Page 414 # 1, 8, 12 and #
2, 5, 11 ( in that order please)

20) On page 414, go through
problems 1 through 12, pick out the ones that have complex characteristic roots
and solve them.

21) Solve the following and
classify as to underdamped/overdamped and, in each
case, draw a sketch of what the solution might look like:

i) y’’ +6y’ +8y =0,

ii) y” +5y’ +5y=0,

iii) ( .5 )y” + ( .7 ) y’ + ( .181 ) y =0 ,

and (iv) (
.23 )y” + ( .8 ) y’ + (3.14) y=0

22) page
422-423 # 13 , 14, and 6

23) (a) (.23) y” + ( 3.14)y =0, y(0) = -10 and y’(0) = 9

(b) y” +16 y = 0, y(0) = 2 and y’(0) =3

Solve these
two problems and express the answer as a shifted cosine ( you
don’t need to compute the phase angle phi). What are the amplitude and period
of the resulting motion?

(c) Solve ( .5) y” + (.7) y’ +( .181) y =0 , y(0) = 2, y’(0) =-3

24) page 422-423 #17 and #7, plus the Prize Problem posed in
class.

25) A handout
on resonance.

26) (a)For the equation: y” + 2y’ +4y = F sin(3t), solve for y_{p}_{ }and compute the response
amplitude, A_{R.}

(b) Same problem except take the
angular frequency of the forcing function to be the resonant frequency.

Hints… the answer to (b) is
roughly twice that of (a).

27) A handout on solving ODEs with
discontinuous RHS by Fourier series.

28) submit an
ODE problem ( with solution) that is suitable for the
final Exam.

29) page 474 # 1 and 2

30) page 478 # 1 and 2

31) page 478 # 3, 4, 5
plus on #8, 9, 10 write down what Euler’s Equation simplifies to ( you don’t
need to solve for the extremal)

Poll results: Out of 43
responses, 39 peeps favored the option of taking the Final on Reading Day. I
will reserve our classroom for 9:30 to 11:30 on that day.

Anyone who wants another day or changes
their mind, please contact me and we’ll make arrangements.

3

30) 333