Toda and Liouville systems are central themes in mathematical physics, providing powerful frameworks for understanding integrable structures, nonlinear dynamics and geometric phenomena. Rooted in the ...

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 ...

Mathematical modeling allows designers to find the best switching frequency, best components, compare two sets of components and optimize the system for any conditions that the application requires ...

Turbulent times This visualization of fluid flow was made using laser-induced fluorescence. (Courtesy: C Fukushima and J Westerweel/Technical University of Delft/CC BY 3.0) The Navier–Stokes partial ...

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 ...

This is the 2nd part of a two course graduate sequence in analytical methods to solve partial differential equations of mathematical physics. Review of Separation of variables. Laplace Equation: ...