PHYSICS 212A
MATHEMATICAL PHYSICS
SPRING 1999
Professor Dennis Silverman

Office: Frederick Reines Hall 2174

Phone: 8245149

Email: djsilver@uci.edu

Office Hours: Mondays, 2:303:30 and Thursdays, 2:003:00 in FRH2174

Lecture: Tuesdays and Thursdays, 9:3010:50, PSCB 210.

Discussion: Friday, 11:0011:50, FRH 2111 or the PC Lab

Required Text: Mathematical Methods of Physics, by Mathews
and Walker, Second Edition, AddisonWesley.

Reference Books: Mathematical Methods in the Physical Sciences,
by Mary L. Boas, Second Edition, Wiley. Mathematical Methods for
Physicists, by Arfken, Third Edition, Academic Press.

Methods of Mathematical Physics, by Courant and Hilbert, Interscience.
Margenau and Murphy.

URL for this course: http://www.physics.uci.edu/~silverma/physics212.html
Homework: Homework will be assigned every week, and is due in class.
Grading

Homework 40%

Midterm 25%. The takehome midterm is assigned below, and is due Monday,
May 17..

Final 35%. This is scheduled for Thursday, June 17, 8:0010:00 AM in the
classroom.

Both exams will be open text book and open notes, but closed to problem
solutions.
Solution of the Black Scholes Equation using the
Green's function for the Diffusion Equation, in
Postscript, in
PDF, and in
HTML.
Mathematica Instruction at UCI

UCI Prof. Herbert Hamber's Mathematica
Course

Mathematica
Notebooks Summary

Mathematica
Summary

The Mathematica Lessons Developed for the Mathematical Physics Course.
Many of the lessons use examples from "Guide to Standard Mathematica Packages",
Version 2.2, Wolfram Research.

Postscript and PDF Versions
 Keyboard Typing of Greek Letters and of Symbols,
Postscript, and
PDF.
 Mathematica Graphics,
Postscript,
and PDF.
 Mathematica Programming,
Postscript,
and PDF.
 Differential Equations,
Postscript,
and PDF.
 Fourier Series,
Postscript,
and PDF.
 Fourier and Laplace Transforms,
Postscript,
and PDF.
 Linear Algebra, Eigenvalues and Eigenvectors,
Postscript,
and PDF.
 Solution to Heat Flow in a Cold Box in one and two dimensions,
Postscript,
and PDF.
 Numerical Methods,
Postscript,
and PDF.
 Statistics,
Postscript,
and PDF.
 BlackScholes Equation Graphs,
Postscript,
and PDF.

Notebook Versions for Mathematica 3.0
The Homepage of Mathematica: Wolfram Research
Numerical Methods Books and Software
The Course Schedule
 The course is currently scheduled to be only one quarter in length.
 It will cover those subjects which were not thoroughly
covered in Classical Mechanics, Quantum Mechanics, or Electrodynamics.
 After in introduction to Mathematica, the Advanced Packages that relate
to the course topics will be covered.
Problem Sets:
 Set 1: Fourier Transforms
 Reading: Chapter 4, pp. 96107.
 Problems on Chapter 4, Due Tuesday, April 13.
 Problem 41.
 Problem 43.
 Problem 45.
 Set 2: Contour Integration
 Reading: Appendix A
 Problems on Chapter 4, Due Tuesday, April 20.
 Justify in detail the steps in the example
(430) on p. 106.
 Problem 47.
 Problem 48.
 Set 3:
 Reading: Ch. 4 pp. 107120
 Problems on Chapter 4, Due Tuesday, April 27.
 Problem 49.
 Problem 410.
 Problem 413.
 Problem 414.
 Set 4: Partial Differential Equations
 Reading, Chapter 8
 Problems on Chapter 8, Due Tuesday, May 4.
 Problem 81
 Problem 83
 Problem 84
 Take Home Midterm
 Problems on Chapter 8 also covering Chapter 4, Due Monday, May 17.
 Set 6: Example of Solving the Heat Equation
 Reading, Material on BlackScholes Equation
 Set 7: Integral Equations
 Reading, Chapter 11
 Problems on Chapter 11, Due Tuesday, May 25.
 Problem 111
 Problem 112
 Problem 114
 Problem 117
 Set 8:
 Problems on Chapter 11, Due Tuesday, June 1.

(1) Find the eigenvalues and eigenfunctions of the kernel (x+y) on the
interval 0 to 1, construct the Resolvent Kernel with the HilbertSchmidt
method, and solve the inhomogeneous equation with the inhomogeneous function
x.

(2) Modify Problem 114 by using the Hermitian kernel cosh(xy), then solve
for the eigenvalues and eigenfunctions, and again construct the Resolvent
Kernal and the solution by the Hilbert Schmidt method.
 Set 9:
 Reading, Handout on Group Theory
 Problems on Chapter 16, Due Thursday, June 10.
 Problem 1613
 Problem 1614
 Problem 1615
 Problem 1616
Topics covered in the previous three quarter course sequence.
Fall Quarter

Chapter 1, Differential Equations

Chapter 4, Fourier Transforms, Appendix A: Contour Integration

Chapter 6, Vectors and Matrices, Eigenvalue Problems

Chapter 7, Special Functions

Mathematica Introduction and Applications
Winter Quarter

Chapter 7, Special Functions

Chapter 8, Partial Differential Equations

Chapter 9, Eigenfunctions, Eigenvalues, and Green's Functions

Chapter 10, Perturbation Theory

Chapter 11, Integral Equations

Mathematica Graphics, Special Functions, and Eigenfunctions
Spring Quarter

Chapter 11, finish Integral Equations

Chapter 5, Further Applications of Complex Variables

Chapter 13, Numerical Methods

Chapter 14, Probability and Statistics

Chapter 16, Group Theory

Chapter 12, Calculus of Variations

Mathematica Programming, Numerical Methods, and Statistics