Maclaurin expansion. Complex numbers and Euler’s formula. Differential equations (DE); first-order DE: variable separable, linear; second-order linear DE with constant coefficients: homogeneous and ...

The new proof broadly consists of three steps: derive the macroscopic theory from the mesoscopic one; derive the mesoscopic theory from the microscopic one; and then stitch them together in a single ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable ...

One-dimensional - Rectangle rule. - Trapezoidal rule. - Simpson's rule. - Gauss-Hermite (TODO) - Gauss-Laguerre (TODO) N-dimensional - Monte Carlo (TODO) - Sparse ...