Partial differential equations (PDEs) form the mathematical backbone for models in physics, engineering, biology and finance. They express relationships between the rates of change of a multivariable ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

Variational analysis of partial differential equations (PDEs) unites the calculus of variations with functional and convex analysis to investigate existence, uniqueness and qualitative properties of ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues. The trajectory of a storm ...