Day: February 20, 2016

Differential Equations

Differential Equations

Differential Equations    02/20/16

 

During one’s study of calculus, one may encounter a peculiar set of derivatives known as Differential equations. Differential equations ae equations in which the derivative of the function is proportional to the function itself, examples including dydx=kyand dydx=y+x. These equations can not be solved through ordinary integration since we would be integrating in respect to a separate variable (yand dx), so one must use a method called separating and integrating, which involves moving the dxto the right side and all of the y’s to the left side (our first example would become dyy=kdx)and then integrate in respect to their variables. This is how the Exponential function comes into existence. Differential equations have an extensive range of application to other branches of science, particularly Physics, Economics, Biology, and Engineering. In fact, Differential Equations are so useful that there is an entire class at Universities dedicated to them that all Physics and Engineering majors must take!

Electric force

Electric force

Electric force 02/20/16

A most usefull riveting concept found in the study of electromagnetism is the electric force. The electric force is defined as the at-a-distance interaction between two charge particles, described by the equation Felec=q1*q24**0*r2 . As one can discern, the Force is proportional to the strength of the two charges, a constant,  and the square of the distance between them. This equation is kindred in nature to the Universal Gravitation equation, substituting mass for electric charge and changing around the constants, a most intriguing symmetry found in physics. However, there is one glaring incongruity in the fact that the electrically charged particles can be either positive or negative, while mass can only exist in a positive value.