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 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 Theory with Repeated Eigenvectors
Asymptotic Stability and Linearization
Asymptotic Stability by Linearization : alternate approach
Undamped Pendulum Energy Landscape
Exercises in 1-d Mechanical Systems
Linearization Unstable and Nonlinear Equilibrium Stable
Derivatives of the Poincare Map
Conjugation of Logistic and Tent Maps
University of Pisa, March-April 2014
K.O. Friedrichs, Symmetric Hyperbolic Linear Differential Equations, CPAM 1954
K.O. Friedrichs, Symmetric Positive Linear Differential Equations, CPAM 1958
K.O. Friedrichs and P.D. Lax, Systems of Conservation Equations with a Convex Extension, PNAS 1971.
Universite de Paris VII,
28 January - 4 February, 2014
Proof of Continuity of Pseudodifferential Operators
Sections II.7 and II.8 of Taylor PDE vol. II
Taylor reflection article with diagonalization argument
Mike Taylor's Commutator Lemma for diagonalization
Nicolas Laillet's course notes, 28 January
Fall 2013 Homework Assignments
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 Neumann Problem, Insulator Boundary Conditions
The Dirichlet Problem in the Disk
Grand Sasso Science Institute, L'Aquila, Italia, May 2018
Meet Maxwell's Equations Outline
Infinitesimal Mean Value Property
Courant-Friedrichs-Lewy, On the partial difference equations of mathematical physics
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
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.
