PHYSICS 212C

MATHEMATICAL PHYSICS

SPRING 1998

Professor Dennis Silverman

Office: PS2 2174

Phone: 824-5149

E-mail: djsilver@uci.edu

Office Hours: Mondays, 2:30-3:30 and Thursdays, 2:00-3:00 in PS2-2174

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.

Also six Mathematica books are on reserve.

URL for this course: http://www.physics.uci.edu/~silverma/physics212c.html

Homework: Homework will be assigned every week, and is due in class.

Grading

• Homework 40%
• Midterm 25%. The midterm is on Tuesday, May 19, 9:30-10:50 AM in class (changed from May 14).
• Final 35%. This is scheduled for Thursday, June 18, 8:00-10:00 AM in the classroom.
• Both exams will be open text book and open notes, but closed to problem solutions.

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

The Homepage of Mathematica: Wolfram Research

• 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", Second Edition, 1991, 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

Problem Sets

• Set 1: Due Friday, April 17.
  • (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 2: Due April 24
  • 13-1
  • 13-3
  • 13-10
• Set 3: Due May 1
  • 13-11
• Set 4: Due May 8
  • 14-1
  • 14-4
• Set 5: Due May 15
  • 14-6
  • 14-8
• Set 6: Due May 22
  • Problem on Binomial to Gaussian in basketball scores.
• Set 7: Due May 29
  • 14-14
  • Problem on maximum likelihood for two Gaussian distributions.
  • Problem on recursion for Chi-squared distributions for even N.
• Set 8: Due June 5
  • 16-13
  • 16-14
  • 16-15
• Set 9: Due June 12
  • 16-16
  • Problem on SU(4) representations using Young Tableau.

Problem Sets for Last Year:

• Set 1:
• 12-1
• 12-3
• 12-6
• 12-9
• Set 2:
• Carry out the calculation of the variational estimation of the energy for the harmonic oscillator, pp. 337-338.
• 12-14
• Set 3:
• 13-1
• 13-3
• 13-10
• 13-11
• Set 4:
• 14-1
• 14-3
• 14-5
• Set 5:
• 14-6
• 14-8
• 14-14
• Set 6:
• 16-13
• 16-14
• 16-15
• 16-16

Course Schedule

The course schedule is intended to roughly parallel the courses in Classical Mechanics, Quantum Mechanics, and Electrodynamics.

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