Notes on Basic Singular Perturbations For Elliptic, Parabolic, Hyperbolic PDE Click here Click here Rough notes on more advanced material Click here
Notes on Strong Localized Peterturbation Theory Click here: Review of Green's functions Click here Review of Legendre Polynomials Click here Two Worked Problems in 2-D Click here
Further Notes on Applications of Strong Localized Perturbation Theory: Ostwald Ripening Click here Biharmonic Equation Click here Low Reynolds Number Flow Click here
Notes on Interface Dynamics in 1-D Click here
Notes on Interface Dynamics in Multi-Dimemsions: Tangential-Normal Coordinates and Derivation of Mullins-Sekerka Flow from Cahn-Hilliard Click here Surface Diffusion in a Chemotaxis model with volume filling Click here
Notes on Homogenization Theory Click here:
Basic Notes on Pattern Formation: Turing Stability Analysis Click here
Notes on Pattern Formation: Case Study of Brusselator Click here
Notes on Pattern Formation: Localized Pulse Solutions Click here
Condensed Notes on Pulse Solutions for an RD System Click here
Notes on Singularities in PDE: Blow-Up Behavior Click here
Notes on WKB For PDE's Click here
Homework 1 (Due Jan. 21: ): Assignment Click here: Solutions Click here
Homework 2 (Due: Feb. ): Assignment Click here: Solutions Click here:
Homework 3 (Due: Feb. ): Assignment Click here: Solutions Click here:
Homework 4 (Due: March): Assignment Click here: Solutions Click here:
Homework 5 (Due: March) : Assignment Click here: Solutions Click here:
Homework 6 (Due: April) : Assignment Click here: Solutions Click here:
Project (Due: April ) : Instructions Click here:
Convection-Diffusion Asymptotics and Strong Localized Perturbation Theory: Click here:
Homogenization References: Click here:
Weakly Nonlinear and Localized Pattern Formation References: Click here:
WKB For PDE's References: Click here: