Professor Dennis Silverman
Office: Frederick Reines Hall 2174
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.
Homework: Homework will be assigned every week, and is due in class.
URL for this course: http://www.physics.uci.edu/~silverma/physics212.html
Midterm 25%. The take-home midterm is assigned below, and is due Monday,
Final 35%. This is scheduled for Thursday, June 17, 8:00-10:00 AM in the
Both exams will be open text book and open notes, but closed to problem
Solution of the Black Scholes Equation using the
Green's function for the Diffusion Equation, in
PDF, and in
Mathematica Instruction at UCI
The Homepage of Mathematica: Wolfram Research
UCI Prof. Herbert Hamber's Mathematica
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,
- 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,
- Black-Scholes Equation Graphs,
Notebook Versions for Mathematica 3.0
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.
- 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.
- 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
(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.
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