Causality and Ordinary Differential Equations
The Steps of Perturbation Theory
Science Text Linearization (Linearization I)
Linearization at an Equilibrium. Peturbation Theory Approach (Linearization II)
Fundamental Theorems of Linear Homogeneous Systems
Zoom Zoom Zoom (Linearization III)
Distinct eigenvalues implies eigenbasis
Phase plane for linear 2 by 2 systems
Ellipse axes, eccentricity, and direction of rotation
Spectral Theorem with Repeated Eigenvectors
Linearization Unstable and Nonlinear Equilibrium Stable
Decreasing Quadratic Forms and Stability
Undamped Pendulum Energy Landscape
Derivatives of the Poincare Map
Conjugation of Logistic and Tent Maps
Fall 2011 Homework Assignments
Image of Circles by 2x2 Matrices
Image of Spheres by Linear Transformations
Outlines of the derivation of everything from Cauchy's Theorem
Laurent Expansion Yields Partial Fractions
Laurent Expansion Yields Fourier Series
Partial Fractions and the Inverse Laplace Transform
More Fourier Analysis from Complex Analysis
The Dirichlet Problem in a Half Space and Corners
The Dirichlet Problem in the Disk
Universite de Paris Nord
janvier 13, 20, 27, fevrier 4, 2011
The infintesimal Laplacian for distributions
Convergence of series for means on balls
The Partial Difference Equations of Mathematical Physics, by Courant, Friedrichs, and Lewy
Fourier Analysis from Complex Analysis
Introduction of geometric optics from Hyperbolic PDE book
Spring energy from Noether's Theorem
A second example of the approximation of geometric optics
Course information
Daily syllabus
m- files and computer related
Wronskian Theorem statement
Integrating factor review
Matlab tutorials
The Steps of Perturbation Theory
K. Miller's Linear Algebra Lecture Notes
To appear in American Mathematics Society Graduate Texts in Mathematics Series. Sorry, no longer on my web page.
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.
Fall 1994 Homework Assignments
Help with the proof of Theorem 6.2-3.
