During the latter part of the 20th century, string theory was put forward as a unifying theory of physics foundations. String ...

Masaki Kashiwara has won the 2025 Abel prize, seen by some as the Nobel of mathematics, for his contributions to algebraic analysis and representation theory ...

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 ...

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. A new ...

Under the hood, mathematical problems called partial differential equations ... the method solves the Fokker-Planck equation, where heat diffuses in a linear way, but there are additional terms ...

Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

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 ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 ...

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 ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

Finding solutions to such equations ... known as partial differential equations (PDEs). Kashiwara's vital work on D-modules, a highly specific area of algebraic analysis involving linear PDEs ...