**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.

- 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 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

- 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.

- 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

- 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

- 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