While other versions may work, the code has been tested and validated only with the versions listed above. Using different versions may lead to unexpected behavior or compatibility issues. Kira is ...

In this video, we explore line integrals in polar coordinates, a key concept in mathematical physics. I’ll guide you through how to set up and evaluate line integrals in polar systems, including ...

Abstract: In the past few years, the intuitionistic fuzzy calculus (IFC) has been proposed, which is based on some basic operational laws of intuitionistic fuzzy numbers (IFNs). The interval-valued ...

Abstract: Mode matching method is here applied to waveguide fields calculated in a transformation optics framework. The proposed approach allows to obtain modes in terms of an expansion onto ...

Learn concepts and practice computing multiple integrals, line integrals, and surface integrals. You can use these live scripts as demonstrations in lectures, class activities, or interactive ...

This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued ...