Jeffrey Rauch's Course Materials
The Wave Equation and Geometric Optics
Universite de
Paris 13, January, 2010
Outline
Course notes
Additional problems
Math 555. Applied Complex Analysis
Fall 2009 Course information.
Fall 2009 Daily Schedule.
Fall 2009 Homework Assignments
Old Exams
Conformal Matrices
Image of Spheres by Linear Transformations
Outlines of the derivation of everything from Cauchy's theorem
Laurent Expansion Yields Fourier Series
Laurent Expansion Yields Partial Fractions
Partial Fractions and the Inverse Laplace Transform.
More Fourier Analysis from Complex Analysis
The Dog on a Leash Principal
The Dirichlet Problem
Fluid Flows
Math 558. Advanced Ordinary Differential Equations
2009 Course information
2009 Daily Syllabus
2009 Homework Assignments
Old Exams
Causality and Ordinary Differential Equations
The Steps of Perturbation Theory
Fundamental Theorem of the Phase Line
Distinct eigenvalues implies eigenbasis
Linearization at an equilibrium. Peturbation theory
approach
Generalized Eigenvectors
Phase plane for linear 2 by 2 systems
Ellipse axes, eccentricity, and direction of rotation
Kronecker's Theorem
Theorems on Gradient Systems
The Turing Instability
Derivatives of the Poincare Map
Math 256. Honors Applied Ordinary Differential Equations
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: >250 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 556. Applied Linear Analysis
Mathematics 556 Notes
Fall 1994 Homework Assignments
Math 571. Numerical Linear Algebra
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. Introduction to Numerical Methods
Syllabus
Textbook's m.files
IEEE floating point standard.
Improved Theorem for 6.4.1.
FFT Handout.
Matrix Norms Handout.
