Mathematical Methods for Scientists (Phys/Math 210)
Lecturer: Daniel Aalberts, TPL 304, x3520, aalberts@williams.edu
Office hours: I am eager to help you understand and enjoy this subject and I am happy to speak
with you about any aspect of the course. Feel free to telephone, email, or pop in at my office.
It is easy to find me as I am typically on campus from 7:45am to 6:30±0:30pm. Late mornings
or afternoons (except M4-6, T12-4) are best.
Lectures: TR 9:55-11:10 in TPL 205. The lectures can only complement other parts of the course.
They can’t be comprehensive, nor are they in any sense sufficient to enable you to fully learn
the material. Developing a thorough understanding of the material and problem solving skills
in any physics or math course also requires reading the text, thinking and talking about the
concepts, and most of all, doing many, many problems.
Textbook: Mary L. Boas, Mathematical Methods in the Physical Sciences, second edition.
Homework Problem sets are normally assigned on Tuesday, due at the beginning of class on the
following Tuesday. Thorough and timely completion of homework is an absolutely crucial
aspect of the course and your performance in it. You are encouraged to discuss homework
problems with classmates but your written solution should be your own work. Please see the
attached honor code statement. Late Homework will not be accepted except by prior (i.e.,
before 4pm Monday) arrangement with the instructor.
Teaching Assistant: Justin Brown or John Mugno will lead help sessions Monday evenings 8:0010:00pm in the physics student common room (TPL 104).
Grading Your grade will be based on homework (15%), three quizzes (60%), and a final (25%).
See page two for the schedule and MARK THOSE DATES!
Honor Code A large fraction of the learning in this course takes place working on the problem
sets, so it is essential that you put a substantial effort into these assignments. Since students
often can learn by discussing the assigned problems with each other, you are welcome to confer
with your fellow students when working on the problems. For optimal learning, there is a
delicate balance between the effort that you make and the amount of assistance you receive
from your fellow students. Try each problem for 15 minutes on your own before asking for
help.
Please observe the following practices:
1. The final write up of all homework is to be done on your own and in your own words.
Direct copying is not permitted.
2. The names of your collaborators should be listed on the assignment.
No collaboration is permitted on examinations. These tests are “closed book,” so during
the tests you should not consult any books or notes written beforehand, except as explicitly
stated by the instructor. If you are in doubt as how the Honor Code applies to any aspect of
this course, please ask the instructor.
1
Phys/Math 210 Agenda
Date
Feb 6
Feb 11
Feb 13
Feb 18
Feb 20
Feb 25
Feb 27
Mar 4
Mar 6
Mar 11
Mar 13
Mar 18
Mar 20
Apr
Apr
Apr
Apr
Apr
Apr
Apr
May
May
May
May
May
May
8
10
15
17
22
24
29
1
6
8
10
15
17-25
Topic
complex numbers
complex functions
Fourier series
more Fourier
Fourier transforms
First order Diff. Eq.
Quiz (z, Fourier)
second order Diff. Eq.
numerical solutions of ODEs
coupled first order ODEs
linear systems
classification of critical points
Quiz (ODE)
Spring Break
series solutions; Legendre’s eqn.
Legendre series
Bessel’s eqn
Bessel functions
scaling and ODEs
Quiz (Series ODE)
PDEs: rectangular boundary
PDEs: cylindrical boundary
PDEs: cylindrical boundary
PDEs: spherical boundary
numerical PDEs
Review
Final (PDE Quiz + recap)
2
Boas
2.1-2.7
2.8-2.16
7.1-7.5
7.6-7.11
15.4, 15.5
8.1-8.4
./
8.5-8.7
handout
handout
handout
handout
./
12.1-12.4
12.5-12.10
12.11-12.14
12.15-12.20
N/A
./
13.1-13.4
13.5
13.5-13.6
13.7
handout
./