Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

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 ...

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...

Delay differential equations (DDEs) extend the classical framework of differential equations by incorporating terms that depend on past states, thus capturing the intrinsic time delays found in many ...

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 ...

homework sets (assigned roughly bi-weekly during the semester). class participation (extra points for helping me to make this class a lively one) projects (written project due at the end of the ...

Fuzzy differential equations (FDEs) extend classical differential equations by incorporating uncertainty through fuzzy numbers. This mathematical framework is particularly valuable for modelling ...

If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential ...

Separation of variables is a powerful method for solving differential equations, enabling the simplification of complex problems into more manageable parts. This video offers a clear and detailed ...