Fall 2011
PH5320 Mathematical Physics Rm 132 Instructor:Beck
Grader: ????
Class: M,W,F 11-Noon
Instructor contact: donald@mtu.edu Office:Room 113,Fisher
Office hours:open (come in as needed)
Text Book: Mathematical Methods for Physicists,6th Edition, Arfken and
Weber
Grading: 50% Homework; 25% Midterm; 25% End term
Exams are open book,open notes,use of homework permitted
SyllabusChapter 9: Differential Equations (100 pages) (+numerical section:hand
out)
Skip pps.538-542 (except BC);sec 9.8
Chapter 10: Sturm-Liouville Theory (53 pages)
MIDTERM
Chapter 11- Bessel Functions (64 pages)
Skip 11.4,11.5;11.6 (note eqns. 11.133,11.134);
Chapter 12- Legendre Functions (50 pages)
Skim 12.7 (Ang.Mom.Ops);12.8 (Addition Theorem);
Sec.12.9 (Integrals of products of 3 Spherical Harmonics). Skip 12.10
(2nd Kind)
Chapter 14 - Fourier Series (6 pages)
Only sec 14.6 (Discrete Fourier Tranform)
Chapter 15- Integral Transforms (70 pages)
Problem Sets
============
Chapter 9: 9.2.13; 9.2.17; 9.3.5; 9.4.1; 9.5.5; 9.6.23; 9.6.25; 9.7.5;
[from numerical handout 8.8.7]
Chapter 10: 10.1.2; 10.1.11; 10.2.6; 10.3.5; 10.4.4; 10.5.10; 10.5.12 (a)
Chapter 11: 11.1.4; 11.1.6; 11.1.15; 11.2.2; 11.2.7; 11.7.5; 11.7.21
Chapter 12: 12.1.4; 12.2.8; 12.3.2; 12.3.11; 12.4.7; 12.5.5; 12.5.15;
12.6.1; 12.6.2; 12.6.6; 12.6.7
Note: For problem 12.4.7 you'll use problem 12.4.4 (without proof). There
is a misprint in the answer for 12.4.4. Instead of (r+n!) It should be (r
+n)!
Chapter 14: 14.6.3; 14.6.5
Chapter 15: 15.3.4; 15.3.9; 15.3.20; 15.4.1; 15.5.6; 15.6.5; 15.6.8;
15.8.5.a; 15.9.3; 15.10.7; 15.10.19b; 15.11.3; 15.12.10; 15.12.13
Other References
================
Mary Boas, Mathematical Methods in the Physical Sciences (a competitor to
Arfken)
H.W.Wyld,Mathematical Methods for Physics,Wiley. Similar level to Arfken
and Weber,but more abstract.
J.Mathews and R.L.Walker,Mathematical Methods for Physics Selective
Coverage (need background).Based on Feynman course.
P.M.Morse and H.Feshbach,Methods of Theoretical Physics,Volumes I and II.
Classic,advanced text,use as a reference.
R.Courant and D.Hilbert,Methods of Mathematical Physics,Volumes I and II.
Advanced text;suitable as reference. Vol. I is less abstract than Vol.II
H.Jefferies and B.S.Jefferies,Mathematical Physics, Cambridge. A
classic,but out-of-print
S.Hassani,Foundations of Mathematical Physics, level similar to Arfken
and Weber
F.B.Hildebrand,Advanced Calculus for Engineers Good on ODE/PDE. Out of
print. Available used.
Handbooks
M.Abramowitz and I.A.Stegun,Handbook of Mathematical Functions, Dover.
Inexpensive.
H.B.Dwight,tables of Integrals and Other Mathematical Data An excellent
set of tables.Out of print.Available used.
Burington,Handbook of Mathematical Tables and Formulae Competitor to
Dwight. Out of print. Available Used.
I.S.Gradshteyn and I.W.Ryzhik,Tables of Integrals and Formulae,Series and
Products (Dover?)
Software
========
MAPLE
MATHEMATICA
You should learn to use one of these while at MTU
Numerical Analysis
==================
F.B.Hildebrand,Introduction to Numerical Analysis A good book.Inexpensive
(Dover). For some reason, Mathematical Physics books (Arfken,Boas) don't
cover numerical methods (nor software methods).This is a significant
failing.
Press,Teukolsky,Vetterling,Flannery,Numerical Recipes in Fortran 77 (or
90),Cambridge,2nd Edition (equations and computer codes). A modern
classic.
Steven E.Koonin,Computational Physics
Harvey Gould and Jan Tobochnik,An Introduction to Computer Simulation
Methods,Parts 1 and 2
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