Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

This analog computer on a chip is useful for certain kinds of operations that CPUs are historically not efficient at, including solving differential equations. Other applications include matrix ...

Course on using spectral methods to solve partial differential equations. We will cover the exponential convergence of spectral methods for periodic and non-periodic problem, and a general framework ...

Elliptic partial differential equations (PDEs) are a class of equations that arise in various fields, including physics, engineering, and mathematics. They are characterized by their smooth ...

Under the hood, mathematical problems called partial differential equations (PDEs) model these natural processes. Among the many PDEs used in physics and computer graphics, a class called second ...

Basic theory for three classical equations of mathematical physics (in all spatial dimensions): the wave equation, the heat/diffusion equation, the Laplace/Poisson equation. Initial value problems - ...

The aim of the course is the study of partial differential equations. The focus will be on first order quasilinear equations, and second order linear equations. The method of characteristics for ...

I work in differential geometry and the application of geometry to the study of partial differential equations. Specifically, my work has focused on conservation laws, Backlund transformations, ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

The members of the group Geometric Analysis and Partial Differential Equations have broad interests in analysis and geometry. Active research topics include quasiconformal analysis and partial ...