Gallery — Math

A proof is given that the summation of all prime numbers can be assigned the value of 13/12, as well as values that can be assigned to the summation of all multiples and all odd multiples.

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.

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.

Primeiras questões respondidas do banco de Cálculo 1 da UFAL.

This project explores the predictability of play-calling of the Simpson College football offense during the years of 2012-2014. The models used to assess the predictability include simple analysis as well as linear and logistic regression.

Suppose we have some topological spaces lying around. How can we build new topological spaces using the old ones? There are four fundamental constructions: subspaces, disjoint unions, products, and quotients. Defining the topologies on each can be done in two ways. One way is through ad hoc definitions. These definitions make some intuitive sense, but look very different from one construction to the next. The other way uses canonical maps. Canonical maps provide a single framework in which all constructions obey the same unifying principle.

A 5th order sine wave approximation

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