Partial Differential Equations
Courses
Heat, wave, and Laplace equations; characteristics, separation, Green’s functions.
Content for this course is still being written. For now, explore the skill map below — every node links to its full page.
Skill map
Each node is a skill; an arrow means "learn this first." Deep-dive links go to the full pages.
The Three Classical Equations…
Heat, wave, Laplace: parabolic, hyperbolic, elliptic.
content coming soon
deep dive ↓The Three Classical Equations
Separation of Variables…
u(x,t)=X(x)T(t) splits a PDE into eigenproblems.
content coming soon
deep dive ↓Separation of Variables
Green's Functions…
Solve inhomogeneous PDEs by convolving with a kernel.
content coming soon
deep dive ↓Green's Functions
Method of Characteristics…
Turn a PDE into ODEs along solution curves.
content coming soon
deep dive ↓Method of Characteristics
Finite Differences…
Replace derivatives with stencils on a grid.
content coming soon
deep dive ↓Finite Difference Methods
Method of Lines…
Discretize space, then integrate ODEs in time.
content coming soon
deep dive ↓Method of Lines
Spectral Methods…
Differentiate via transforms for exponential accuracy.
content coming soon
deep dive ↓Spectral Methods
Operator Splitting…
Alternate the evolution of decomposed operators.
content coming soon
deep dive ↓Operator Splitting