Math 4362, Partial Differential Equations

Spring 2024

John Zweck

Course Materials

Lecture Notes

Homework Assignments

Past Exams

Resources for Essay

• Transport equations
• Telegrapher's equation
• Transport equations on networks and graphs
• Nonlinear transport equation
• Burger's equation
• Flow in porous media equations
• Euler-Tricomi equations for transonic flow
• Euler conservation equation for inviscid flows
• Heat (diffusion) equation
• Stochastic PDE's
• Black-Sholes equation in mathematical finance
• Fokker-Planck equations for evolution of probability density functions
• Wave equation (acoustic and elastic)
• Maxwell's equations for electromagnetic waves (light)
• Schroedinger equation in quantum mechanics
• Klein-Gordon and Dirac equations for relativistic wave propagation
• Euler-Bernoulli equation for vibrating beam
• Biharmonic equation
• Equations of linear elasticity in continuum mechanics
• Helmholtz equations for time-independent wave propagation
• Hamilton-Jacobi equations in classical mechanics
• Navier-Stokes equations in fluid dynamics
• PDE's for fracture mechanics
• Laplaces equation
• Poisson's equations and applications to electric and gravitational potentials
• Reaction diffusion equations for pattern formation
• Allen-Cahn equation for materials science applications
• Linear dispersive equation in fiber optics
• Nonlinear wave equations
• KdV equation for shallow water waves
• Nonlinear Schroedinger equation for modeling propagation of light in optical fiber
• Ginzburg-Landau equation for modeling fiber lasers and Bose Einstein condensates
• Boussinesq equation for water waves
• Perona-Malik equation to reduce noise in images
• Eikonal equation from geometric optics
• Minimal surface equation
• Harmonic maps in differential geometry
• Geometric heat flows
• Mean curvature flow in differential geometry
• Ricci flow in Riemannian geometry
• Einstein equations in general relativity

Demos and Matlab/Python Code