Jeffrey Rauch's Course Materials

 


The Wave Equation and the Laws of Geometric Optics

Universite de Paris 13, January-February 2008

Outline (pdf)

Course Notes (pdf)


Math 256 Materials

Course information

Daily syllabus

Homework

m- files and computer related

Wronskian Theorem statement

Integrating factor review

Matlab tutorials

K. Miller's Linear Algebra Lecture Notes


Hyperbolic Partial Differential Equations and Geometric Optics

From old Nonlinear Geometric Optics notes, (Warning: 219 pages), pdf version.

Nonlinear Resonance

Universita di Pisa, March-April 2007

Outline

Chapter 9. The first classes.

Chapter 10. April 12.

Chapter 6. Sections 6.4 and 6.6 are cited in Chapter 9.

Chapter 11. April 19,26.


Dispersive Properties of Hyperbolic Partial Differential Equations

Universita di Pisa, March-April 2006

Outline.txt

Notes.pdf


Math 558 Materials

Syllabus

Homework assignment 1

Remarks on existence and uniqueness

The eigenbasis theorem

Homework 1 Problem 3 Solution

Midterm solutions

Theorems on Gradient Systems

Derivatives of the Poincare Map

2006 Final Exam


Math 556 Materials

Mathematics 556 Notes

Fall 1994 Homework Assignments


Math 555 Materials

Fall 2002 Outline. (Postscript), (PDF).

Laurent Series Yield Partial Fractions. (Postscript), (PDF).

Laurent Series Yield Fourier Series. (Postscript), (PDF).

Band Limited Signals (Postscript), (PDF).

Fourier Coefficients of Periodic Analytic Functions. (Postscript), (PDF).

The Dog on a Leash Principal (Postscript), (PDF).

The Laplace Transform and Partial Fractions (Postscript), (PDF).

Fall 2001 Midterm Exam (Postscript), (PDF).

Fall 2002 Midterm Exam (Postscript), (PDF).

Fall 2001 Final Exam (Postscript), (PDF).

Fall 2002 Final Exam (Postscript), (PDF).

Fall 2002 Homework Assignment 1. (Postscript), (PDF).

Fall 2002 Homework Assignment 2. (Postscript), (PDF).

Fall 2002 Homework Assignment 3. (Postscript), (PDF).

Fall 2002 Homework Assignment 4. (Postscript), (PDF).

Fall 2002 Homework Assignment 5. (Postscript), (PDF).

Fall 2002 Homework Assignment 6. (Postscript), (PDF).

Fall 2002 Homework Assignment 7. (Postscript), (PDF).

Fall 2002 Homework Assignment 8. (Postscript), (PDF).

Fall 2002 Homework Assignment 9. (Postscript), (PDF).

Fall 2002 Homework Assignment 10. (Postscript), (PDF).

Fall 2002 Homework Assignment 11. (Postscript), (PDF).


Math 571 Materials

Outline.

Help with the proof of Theorem 6.2-3.

Homework Assignment 1.

Homework Assignment 2.

Homework Assignment 3.

Homework Assignment 4.

Homework Assignment 5.

Homework Assignment 6.

Homework Assignment 7.

Homework Assignment 8.

Homework Assignment 9.

Homework Assignment 10.

Homework Assignment 11.

Homework Assignment 12.

Study problems.


Math 471 Materials

Syllabus

Textbook's m.files

IEEE floating point standard.

Improved Theorem for 6.4.1.

FFT Handout.

Matrix Norms Handout.