Gallery — Math

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.

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.

Chapitre 2, Peip2, Polytech'Nice Sophia, sans les sch\'emas et applications sch\'ematis\'ees

Problem #2

A 5th order sine wave approximation

Voor huiswerkopdrachten

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

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.

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.