The Code is an ancient matrix system built up of monuments all across the globe. These monuments include megalithic stone works, pyramids, circular works, effigies, and ancient earth mound. Each structure

In this tutorial, we'll work through 2 different approaches to solving the integral of sin3(ax). Now, there maybe more ways of approaching this problem, but these were the most obvious to me. Using a

We can apply the principle of exponential decay to find equations that model the charge remaining in a capacitor as it is discharged through a resistor. The circuit diagram is shown below... When the switch

What I love about mathematics is some of the very creative and ingenious methods that someone has come up with to find solutions to perplexing problems. The integral of √(a2 - x2) is a great example one

Inasmuch as the differential equation dy/dx = ky models exponential growth, it follows that dy/dx = -ky models exponentially decaying processes. A exponential decay process, which is a slowing reduction

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With the differential equation dy/dx = ky, we found the general solution to be y(x) = Aekx. We worked this out in my last post. This equation lends itself to the modelling of exponential growth. Now in

In this video, we work through the process of solving for the general solution of a simple separable differential equation: The general solution is obtained by separating the variables so that all y's

Differential Equations are one of the most useful tools developed in mathematics. You'll see them everywhere in Engineering, Physics, Biology, etc. for the modelling of phenomena. So what are differential

The term 1/(a2 + x2) is purely algebraic. However, its integral is trigonometric. When you look this up in a table of integrals, you'll find the integral: ∫1/(a2+x2)dx = (1/a)arctan(x/a) + C How is this

In this video, we work through the derivation of the reduction formula for the integral of cosn(x) or [cos(x)]n. The first step is to rewrite the integral as: ∫cosn(x)dx = ∫cosn-1(x)cos(x)dx Thus we have

In this video, I work through the steps to solving the integral of cos3(x) or [cos(x)]3. Note that because cos(x) is a function of x, not a mere polynomial, we can't just use the power formula as a method

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