Split PDE modules in syllabus

Author: Daniel Precioso, PhD

syllabus.qmd

@@ -6,7 +6,7 @@ format: html
 
 ## Program
 
-This site is organized around **eight core modules** plus one extra Lorenz attractor module.
+This site is organized around **nine core modules** plus one extra Lorenz attractor module.
 
 The sidebar navigation is the ground-truth order for the material, and this page follows the same structure.
 
@@ -30,9 +30,13 @@ Model flocking and alignment in continuous space. The main case studies use Vics
 
 Represent systems as graphs with `networkx`. You measure connectivity and centrality, generate standard graph models, and simulate SIS and SIR spreading on synthetic and real networks.
 
-### Partial Differential Equations
+### PDEs in 1D
 
-Discretize reaction-diffusion systems in one and two spatial dimensions. You build Laplacians with finite differences, study Turing instability, and simulate Gierer-Meinhardt and Gray-Scott pattern formation.
+Discretize reaction-diffusion systems on an interval. You build finite-difference Laplacians, apply boundary conditions, study Turing instability, and use the linearized mode picture to predict which spatial patterns should grow.
+
+### PDEs in 2D
+
+Extend the same workflow to rectangular grids. You reuse the vectorized solver structure in two spatial dimensions, compare boundary conditions, and simulate Gierer-Meinhardt and Gray-Scott pattern formation.
 
 ### Cellular Automata