Physics 116B Mathematical Methods in Physics Spring 2005

MWF, 11:00—12:10 pm, Earth and Marine Sciences B214.

Instructor: Robert Johnson

Office: 323 Natural Sciences II; Phone 459-2125

E-mail: rjohnson@scipp.ucsc.edu

Office hours: MWF 3:30—4:45 pm, or by appointment.

Course Web site: http://scipp.ucsc.edu/~johnson/phys116b/phys116b.htm

TA: Lucas Winstrom

Office: 217 NS-II; Phone 459-5119 Office hours: 1:00 to 2:00 pm Tuesday and Thursday

E-mail: luke@physics.ucsc.edu

Discussion Section: Thursdays, 6:00 to 7:30 pm, ISB 231

Textbook: Mathematical Methods for Scientists and Engineers, Donald McQuarrie.

Exams: Midterms: Monday, April 11 and Wednesday, May 11

Final: Wednesday, June 8, from 8:00 to 11:00

Week	Dates	Topics	Chapter	Homework due
1	Mar 28 Mar 30 Apr 1	Vector spaces Inner product spaces Complex inner product spaces	9.5 9.6 9.7
2	Apr 4 Apr 6 Apr 8	Orthogonal and unitary transformations Eigenvalues and eigenvectors Change of basis	10.1 10.2,10.3 10.4	#1
3	Apr 11 Apr 13 Apr 15	Diagonalization of matrices Quadratic forms The power series method for differential eqns	10.5 10.6 12.1	#2
4	Apr 18 Apr 20 Apr 22	Midterm Exam 1 (covering HW 1 and 2) Ordinary and singular points Series solution near an ordinary point	12.2 12.3	#3
5	Apr 25 Apr 27 Apr 29	Solutions near regular singular points Bessel’s equation and functions Legendre polynomials	12.4 12.5,12.6 14.1	#4
6	May 2 May 4 May 6	Orthogonal polynomials Sturm-Liouville theory Eigenfunction expansions	14.2 14.3 14.4	#5
7	May 9 May 11 May 13	Fourier series as eigenfunction expansions Midterm Exam 2 (covering HW 3, 4, and 5) Sine and cosine series	15.1 15.2	#6
8	May 16 May 18 May 20	Convergence of Fourier series Fourier series and ODE The Euler equation	15.3 15.4 20.1	#7
9	May 23 May 25 May 27	Laws of physics in variational form Variational problems with constraints Variational formulation of eigenvalue problems	20.2 20.3 20.4	#8
10	May 30 June 1 June 3	Holiday Multidimensional variational problems Wrap-up and review	20.5	#9
11	June 8	Final Exam at 8:00 am

Please at least read the relevant sections of the textbook before coming to lecture. I think that this textbook is very readable, with good explanations. You will be responsible for the listed textbook sections, even if I do not cover every detail in lecture.

A set of homework problems will be given out each week, due more-or-less a week later, for a total of nine assignments. You may collaborate on the homework, but your final solutions should be written up by yourself (I don’t want to see multiple exact copies of the same solution). Do keep in mind that if you make a habit of letting somebody else do all the thinking for you, then you will not learn to solve problems and will not be well prepared for the exams. Take some time to struggle with a problem yourself before asking somebody else how to do it. Many, if not most, of the problems in this course will be straightforward exercises, however. There will be lots of them assigned, but hopefully most of them will not involve much struggle.

You are also encouraged to seek help on the homework or the math concepts and methods from myself and the teaching assistant. While my office hours are the most convenient time for me to meet with you, if you have an urgent question that cannot wait, you are welcome to look for me at other times or else send me e-mail. Keep in mind that I expect on most Tuesdays and Thursdays to be working at Stanford, but I usually will be available by e-mail.

Grades and evaluations will be determined from the homework, the midterm exam, and the final exam, with the following approximate weights:

· Homework: 20%

· Midterm exams: 20% each

· Final exam: 40%

Homework will be graded as follows for each problem:

· Unless otherwise noted on the assignment, 4 points will be awarded for a correct solution, including showing all steps (giving just the answer is generally insufficient, especially since many answers are given in the back of the textbook). In most cases no partial credit will be given in the case of an incorrect solution; exceptions to this rule will be noted on the assignment and will be restricted to lengthy, difficult calculations.

· One extra point for a good presentation: neat, complete, easy to follow, with explanations written in English where appropriate.

Exams solutions will be given partial credit where warranted. All exams will be closed book, with no notes allowed. I expect you to learn definitions and equations at least well enough to have them in your short-term memory. In the rare case that a long, esoteric equation is needed, I will print it on the exam.

I have not taught this course before. Indeed, it is in a completely new 3-quarter format this year, so I may have to adjust the syllabus as we go. The recommended 116ABC syllabus does not follow very well the organization of the textbook. Nevertheless, I intend to try to follow the textbook sequence to the maximum extent possible. To that end, I am taking the initiative to move Legendre and Bessel functions from 116C into this course and to move asymptotic series and special functions from this course into 116C.

Reserves: in addition to the course textbook, the previous textbook, Mathematical Methods in Physical Sciences by Boas, is also on reserve in the science library.