Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

We were always taught that the fundamental passive components were resistors, capacitors, and inductors. But in 1971, [Leon Chua] introduced the idea of a memristor — a sort of resistor with memory.

Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and ...

Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

In this article we study a class of stochastic functional differential equations driven by Levy processes (in particular, α-stable processes), and obtain the existence and uniqueness of Markov ...

Solutions of the n-th order linear ordinary differential equations ${\left( {z + b} \right)^1}\prod\limits_{k = 1}^{n - 1} {\left( {z + {a_k}} \right){\varphi _n ...

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures. Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations For ...