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/ ( x2 +y2 z2 )

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) = N0 /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) = TA + ( T0 – TA ) e - k t . Then solve for k using the fact that when t = 10, T = 100o. 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 yp and compute the response amplitude, AR.

(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