In the past week, I studied Differential Equations through an MIT Online Open Course, which can be found here:
In this blog, I will introduce Differential Equations as well as some of the methods of solving or visualizing them. I will start from the place where most students left out since Calculus II to make it more comprehensible.
Differential Equations, also known as DE, means “an equation involving derivatives of a function of functions” (dictionary.com). Differential Equations have a broad application in subjects like Physics, Engineering, and Biology, which will be discussed in depth in my future blogs. The first several blogs, however, will be focusing on the math behind differential equations including how to solve and visualize the formulas.
One simple example of DE is , in which x is the independent variable and y is the dependent variable. Notice that taking integral is not a way to find a general solution of y; instead, we must employ a method called “Separation of Variables”. Continue reading