This note covers the following topics: Hyperbolic conservation
laws, stability of hyperbolic waves, heat equation, burgers waves, burgers
greens functions, stability of diffusion waves, stability of shock waves,
estimates of the greens function, stability of rarefaction waves, stability of
rarefaction waves.
Author(s): Tai-ping Liu, Shih-hsien Yu
and Yanni Zeng
These notes present numerical methods for conservation laws and related
time dependent nonlinear partial differential equations. The focus is on both
simple scalar problems as well as multi dimensional systems.
This note covers the following topics: introduction, calculus of
variations basics, the action, Lagrangian and lagrangian density, particles,
fields, canonical variables, the euler-lagrange equations and dynamics in
particles, fields, Noether's theorem and conservation laws.