PHYSICS 212B

MATHEMATICAL PHYSICS

WINTER 1998

Professor Dennis Silverman

Office: PS2 2174

Phone: 824-5149

E-mail: djsilver@uci.edu

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

Lecture: Tuesdays and Thursdays, 9:30-10:50, PST (trailer) 100

Discussion: Friday, 11:00-11:50, FRH 3111 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/physics212b.html

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

Grading

• Homework 40%
• Midterm 25%. The midterm has been moved to Thursday, Feb. 12, 9:30-10:50 AM in class.
• Final 35%. This is scheduled for Thursday, March 19, 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 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

• 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 for This Year:

• Set 1:
• Reading, Chapter 7, pages 178-198
• 7-16
• 7-22
• 7-23
• 7-26
• 7-27
• Set 2: Due Friday, January 30.
• Reading, Chapter 8
• 8-1
• 8-4
• 8-7
• Set 3: Due Friday, February 6.
• 8-19
• 8-20
• Plot in 3 dimensions for various times t the results for the heated cold cube, Eqn. 8-59.
• Set 4: Due Friday, February 20.
  • Plot the solution to the Black-Scholes eqn. of omega/c as a function of x/c for times of 0, 1/4, 1/2, 3/4, and 1 times t*=90 days. Take r=0.05/365 and v^2/2r = 0.3.
• Set 5: Due Friday, February 27.
• 9-3
• 9-5
• 9-8
• Derivation on pp. 271-273.
• Set 6: Due Friday, March 6.
• 10-1
• 10-5
• 10-6
• 10-10
• Set 7: Due Friday, March 13.
• 11-1
• 11-2
• 11-4
• 11-7

Course Schedule

The tentative 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, Eigenfunctions, and Programming

Spring Quarter

• Chapter 12, Calculus of Variations
• Chapter 13, Numerical Methods
• Chapter 14, Probability and Statistics
• Chapter 16, Group Theory
• Chapter 5, Further Applications of Complex Variables