synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
Roughly, “integrating” a partial differential equation means to find a solution for it, usually understood with special properties, such as having prescribed boundary data (initial data), and/or having “closed form”, such as expression by quadratures (“integrable systems”) and/or having prescribed domain (e.g. over infinitesimal neighbourhoods in formal integrability). A PDE is “integrable” in a prescribed sense if it admits solutions in this prescribed sense.
Hubert Goldschmidt, Integrability criteria for systems of nonlinear partial differential equations, Journal of Differential Geometry 1 (1967) 269–307 (Euclid)
Maciej Zworski, Numerical linear algebra and solvability of partial differential equations, Communications in Mathematical Physics 229 (2002) 293–307
Created on October 10, 2017 at 04:28:07. See the history of this page for a list of all contributions to it.