PHYSICS 212A

MATHEMATICAL PHYSICS

SPRING 1999

Professor Dennis Silverman

Office: Frederick Reines Hall 2174

Phone: 824-5149

E-mail: djsilver@uci.edu

Office Hours: Mondays, 2:30-3:30 and Thursdays, 2:00-3:00 in FRH-2174

Lecture: Tuesdays and Thursdays, 9:30-10:50, PSCB 210.

Discussion: Friday, 11:00-11:50, FRH 2111 or the PC Lab

Required Text: Mathematical Methods of Physics, by Mathews and Walker, Second Edition, Addison-Wesley.

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

Grading

• Homework 40%
• Midterm 25%. The take-home midterm is assigned below, and is due Monday, May 17..
• Final 35%. This is scheduled for Thursday, June 17, 8:00-10:00 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.
• Black-Scholes Equation Graphs, Postscript, and PDF.
• Notebook Versions for Mathematica 3.0
• Keyboard Typing of Greek Letters and of Symbols
• Mathematica Graphics
• Mathematica Programming
• Differential Equations
• Fourier Series
• Fourier and Laplace Transforms
• Linear Algebra, Eigenvectors and Eigenvalues
• Solution to Heat Flow in a Cold Box in one and two dimensions.
• Numerical Methods
• Statistics
• Black-Scholes Equation Graphs

• Computational Physics Course With Mathematica at Univ. of Western Australia
• The Integrator: does integrals for you on the web
• Trigonometric and Exponential Functions
• Higher Functions in Mathematica
• "Mathematica: A System for Doing Mathematics by Computer", Fourth Edition, 1999, by Wolfram, on-line
• MathReader (free)

Numerical Methods Books and Software

• Numerical Recipies in Fortran 77: The Art of Scientific Computing, (in postscript)
• Numerical Recipies in C: The Art of Scientific Computing , (in postscript)
• both by William H. Press, Saul. A. Teukolsky, William T. Vetterling, and Brian P. Flannery.
• Netlib Repository
• SLATEC Software Library
• Fourier Series Applet

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. 96-107.
• Problems on Chapter 4, Due Tuesday, April 13.
• Problem 4-1.
• Problem 4-3.
• Problem 4-5.
• Set 2: Contour Integration
• Reading: Appendix A
• Problems on Chapter 4, Due Tuesday, April 20.
  • Justify in detail the steps in the example (4-30) on p. 106.
  • Problem 4-7.
  • Problem 4-8.
• Set 3:
• Reading: Ch. 4 pp. 107-120
• Problems on Chapter 4, Due Tuesday, April 27.
  • Problem 4-9.
  • Problem 4-10.
  • Problem 4-13.
  • Problem 4-14.
• Set 4: Partial Differential Equations
• Reading, Chapter 8
• Problems on Chapter 8, Due Tuesday, May 4.
  • Problem 8-1
  • Problem 8-3
  • Problem 8-4
• Take Home Midterm
• Problems on Chapter 8 also covering Chapter 4, Due Monday, May 17.
  • 8-10
  • 8-18
  • 8-19
  • 8-20
• Set 6: Example of Solving the Heat Equation
• Reading, Material on Black-Scholes Equation

• Set 7: Integral Equations
• Reading, Chapter 11
• Problems on Chapter 11, Due Tuesday, May 25.
  • Problem 11-1
  • Problem 11-2
  • Problem 11-4
  • Problem 11-7
• 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 Hilbert-Schmidt method, and solve the inhomogeneous equation with the inhomogeneous function x.
• (2) Modify Problem 11-4 by using the Hermitian kernel cosh(x-y), 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 16-13
  • Problem 16-14
  • Problem 16-15
  • Problem 16-16

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