THE main work of mathematical physicists is to represent the sequence of phenomena in time and space by means of differential equations, and to solve these equations. Even the revolution effected by ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

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 ...

In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular ...

Japanese mathematician Masaki Kashiwara wins Abel Prize for contributions to algebraic analysis and representation theory at ...

Physics-informed neural networks (PINNs) represent a burgeoning paradigm in computational science, whereby deep learning frameworks are augmented with explicit physical laws to solve both forward and ...

The honor, like a Nobel Prize for mathematics, was given this year to Luis Caffarelli for his work on partial differential equations. By Kenneth Chang As a mathematician, Luis A. Caffarelli of the ...

The course is devoted to analytical methods for partial differential equations of mathematical physics. Review of separation of variables. Laplace Equation: potential theory, eigenfunction expansions, ...

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, ...

Researchers from The University of New Mexico and Los Alamos National Laboratory have developed a novel computational framework that addresses a longstanding challenge in statistical physics.