Gallery — Math

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

Voor huiswerkopdrachten

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)

A brief (lets not kid ourselves its long) introduction to the continuous and discrete wavelet transforms. Comments on implementations on the computer using MATLAB and other software is also included.

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.

This work is going to analyze the Forced Van Der Pol's Equation which is used to analyze the electric circuit. In 1927, Balthasar Van Der Pol observed the stable oscillation and heard some irregular noise in vacuum tube circuit. He then proposed the Forced Van Der Pol's Equation to analyze the circuit and suggested the concept of limit cycle and Chaos to explain his observation. In this work, We would like to analyze behavior of the model by observing the phase space, time series, bifurcation diagram and power spectrum. Those points in the figures are calculated by Runge-Kutta Method with the aid of MATLAB. For a better understanding, the RLC circuit, which is a electric circuit consisting the a resistor, an inductor and a capacitor, will be used as an example for explaining the properties. Apart from electric circuit, the Forced Van Der Pol's Equation can be applied to dynamic systems in different aspect, such as the artificial heart, economic market and so on. Therefore, we suggest this work to all students since the Forced Van Der Pol's Equation can be applied to many majors, like Mathematics, Physics, Economics, Sociology, Biology, Engineering and so on.

Various geometrical shapes are described, for which the numerical value of the perimeter is the same as that of the area. Cases of one or two parameters are explored.