


Instructor: 
Raymond Frey , Wil 405, 3465873, rayfrey@uoregon.edu 
Lectures:  MW 2:003:20, Wil 318 

Office hours:  Mon 1112:30, Fri 23 
Text:  Arfken and Weber, Mathematical Methods for Physicists, 6th Ed. 
Prerequisite:  Vector calculus, ordinary differential equations. (Check
with Prof Frey if questions.) 
WWW:  http://physics.uoregon.edu/~rayfrey/410/
(this page) 
Grading:  Midterm Exam (25%), Homework
(40%), Final
Exam
(35%) 
Other Resources:  Homework Solutions  links to pdf
files in table below 
Date  
Dec 4 
Final exam
solutions 
Dec 1 
Final exam
practice solutions. (Note that all of the homework solutions
and summaries are available from links below.) 
Dec 1 
Office hours during finals
week: Mon: 9:3011:30, 1:303:30; Tues: 10noon. 
Nov 30 
Final exam
practice problems (Note: there is a type on problem 4.) 
Oct 29 
Midterm
solutions 
Oct 20 
HW #4 posted below 
Oct 18 
Practice Midterm Exam: exam  solutions 
Oct 18 
links to all HW solutions in
table below 
Oct 17 
Midterm exam is Monday Oct
22. No class Weds Oct 24. We will make up this class on
Fri Nov 30 at 2:003:20 
Oct 9 
short summaries for weeks 13 


Text Chs. 
("Problems" from text ) 


Sep 24 
Orientation, goals. Review of some vector material. Finite linear spaces: matrices and matrix equations. Summary page. 
3 
#1: 3.1.1 , 3.1.2; 3.2.3, 3.2.20, 3.2.32, 3.2.34, 3.2.36; 3.3.9 
10/1, in class 
HW1 Solutions 
Oct 1 
Similarity transformations;
hermitian and unitary operators; eigenvalue problems Summary page 
3 
#2:
3.3.12, 3.3.13; 3.4.3, 3.4.6, 3.4.12; 3.5.6, 3.5.8, 3.5.12, 3.5.20; 3.6.9 
10/10 (W), in class 
HW2 Solutions 
Oct 8 
hermitian operators, unitary
transformations, and eigenvalue problems (contd) Summary page 
3 
#3:
3.5.9, 3.6.20; 1.15.1, 1.15.6, 1.15.9; 9.7.6, 10.1.1 
10/18 by 5PM, or 10/17 in class 
HW3 Solutions 
Oct 15 
Dirac delta fn (Ch 1.15);
overview of 2nd order ODE (Ch 9); Green's fns I (Ch 9.7); SturmLiouville systems intro Summary pages 
1.15, skim 9; 10.1,10.2 
#4:
10.1.8, 10.1.13, 10.1.16, 10.1.17; 10.2.5, 10.2.6 
11/1 (Th) 
HW4 Solution 
Oct 29 
SturmLiouville systems,
Hermitian operators Summary pages 
10.1,10.2 
#5:
10.4.4; 12.3.2, 12.3.5; 14.3.4, 14.3.12, 14.3.14 
11/9 
HW5 Solutions 
Nov 5 
generalized Fourier series,
completeness Summary pages 
10.4 10.5 12.3,14.3 
#6:
10.1.11a, 10.2.3, 10.5.12; 15.3.5, 15.3.9, 15.3.16, 15.5.5, 9.7.16 
11/21 
HW6 Solutions 
Nov 12 
Green's fns II (brief); Fourier transforms; transformation of differental equations; convolution; transfer fns Summary pages 
15,115.7 

Nov 19 
contour integration (brief) Summary pages for contour integration 
6.4,6.5,6.6 7.1 
#7:
15.3.4, 15.3.10, 15.4.3, 15.6.8, 15.6.12 
11/30 5 PM 
HW7
Solutions 
Nov 26 
countour integ., Fourier
transform applications (contd); Summary review 

Dec 4, Tue 15:1517:15 
Final Exam, Wil 318 
Course
Description and Plan
(approximate):
The primary goal of the course is
provide the
mathenatical background necessary for a 400level course in quantum
mechanics.
We will start by covering linear algebra of finite spaces (mostly Ch 3
of the text).
We will then move to the heart of the course: Ch 10 of the text, from
which we see how a certain class of differential equations are
connected to the infinite function spaces commonly used in QM and other
subjects.
We will look at some of the corresponding special functions, but will
focus more on a familiar example  Fourier series  and then
generalize this to the Fourier transform and look briefly at other
integral transforms.
Details are below. The exact course plan and material will depend
somewhat on student background and interest.
Summary notes written by Prof Frey will be
provided.
Main
topics to be covered:
There will be one midterms and one final exam. Exams will be closed
book, but the generally useful equations and information will be
provided.
Practice exams and solutions will be provided
approximately one week before an exam.