MWF 1:40-2:35 ES 146
Instructor: Professor Edward Thomas ES 132F
Best way to reach me is by email: email@example.com
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.
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!!
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?
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