Gallery Items tagged Math

Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
The differential wave equation can be used to describe electromagnetic waves in a vacuum. In the one dimensional case, this takes the form $\frac{\partial^2\phi}{\partial x^2}-\frac{1}{c^2}\frac{\partial^2\phi}{\partial t^2} = 0$. A general function $f(x,t) = x \pm ct$ will propagate with speed c. To represent the properties of electromagnetic waves, however, the function $\phi(x,t) = \phi _0 sin(kx-\omega t)$ must be used. This gives the Electric and Magnetic field equations to be $E (z,t) = \hat{x} E _0 sin(kz-\omega t)$ and $B (z,t) = \hat{y} B _0 sin(kz-\omega t)$. Using this solution as well as Maxwell's equations the relation $\frac{E_0}{B_0} = c$ can be derived. In addition, the average rate of energy transfer can be found to be $\bar{S} = \frac{E_0 ^2}{2 c \mu _0} \hat{z}$ using the poynting vector of the fields.
Eric Minor

Estudio del proceso termodinámico en una máquina de expreso
Estudio de los procesos termodinámicos que conllevan una máquina de expreso. Se utiliza solo agua, sin el filtro de café para utilizar solo la densidad del agua. Se encuentra que es similar a un proceso de Carnot, pero como un ciclo abierto.
Luis Alberto González José

Th\'eorie cin\'etique des gaz parfaits.
Chapitre 2, Peip2, Polytech'Nice Sophia, sans les sch\'emas et applications sch\'ematis\'ees
Rémy Collie

CS 6505 Readiness Assessment - Problem 2
Problem #2
Laura Hamilton

Sine approximation
A 5th order sine wave approximation
Pepijn de Vos de Vos

Inleveropgaven Basiswiskunde, Week 2
Voor huiswerkopdrachten
Sliem el Ela

Math 333 Weekly Homework Template
This is a template for students from Math 333 at Hood College to use for weekly homework submission. (Fall 2018)
Jill Tysse

Estudio de los factores de disipación de la mica-epoxi en pruebas de calentamiento para placas de circuitos eléctricos
Comprensión de un estudio realizado en la mica-epoxi para placas de circuitos. El estudio consistió en pruebas de resistencia para medir el desgaste en el tiempo del material y así determinar su tiempo de vida aproximado.
Luis Alberto González José

Mimetic postprocessing for LFRic
We describe what mimetic interpolation is and why it is critical for some pre- and post-processing tasks. A simple test case shows how using bilinear interpolation for a flux calculation introduces numerical errors that depend on the grid, the number of segments and the number of quadrature points. In contrast, mimetic interpolation will return the exact result regardless of the grid resolution and the number of segments.
Alex Pletzer and Wolfgang Hayek and Jorge Bornemann