I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. In this video, we derive a formula for the integration of the powers of cosecant of

In my previous post, we discussed the principles of mechanical resonance. In this post, we'll look into another vibratory characteristic called "beats", which can also be described by our undamped,

Figure 1. Sound shatters a wine glass(source: YouTube, creative commons licence) In engineering and acoustics, second order differential equations can give us a fascinating insight into mechanical vibrations.

Figure 1 below shows a schematic of the mass-spring-damper model to include an applied external force, F. Figure 1.Mass-Spring-Damper system with external force In post #5 of this series on solving 2nd

Let's work through another example on how to solve non-homogeneous 2nd order differential equations. This is our final example before we look at practical applications of this method of solving ODE's.

In this post, we'll work through yet another example of the method of undetermined coefficients for solving non-homogeneous ordinary differential equations. Figure 1. The particular solution to equation

In the last post, we went through the process of finding the solution to a 2nd order nonhomogeneous differential equation with the non-zero term r(x) as a polynomial. In this post we'll work through an

In my last post, I stated something rather paradoxical about solving non-homogeneous differential equations: ...to find a solution to the non-homogeneous equation, we need to find a solution to the

Generally, a non-homogeneous, 2nd order, linear, ordinary differential equation can be written in the form... Equation (1) is deemed to be non-homogeneous because the term on the right-hand side of the

In this post, we will use a bit of plane geometry and algebra to derive the formula for the perpendicular distance from a point to a line. Now, the process I'm going to go through with you is not the most

In this video, we work through the process of solving the integral of ∫cos^4(x)dx. The main aim is to reduce the power down to unity. We can do this either by using the half-angle formula like so... cos^4(x)

In the last few posts, we've been studying the mathematical modelling of car suspension systems (i.e. mass-damper-spring systems). So far, we've explored the under damped, and critically damped settings

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. In this video, we work through the derivation of the reduction formula for the integral

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. In this video, we go through the process of solving the linear equation: There are

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. In this video, we look at how to solve the equation: This is problem where we will

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. In this video, we will solve the integral of tan^3(x)... The first step is to reserve

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. In this video I demonstrate how to find the integral or antiderivative of the natural

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. In this video, I demonstrate how to find the anti-derivative or the integral of tan2(x).

In the mathematical modelling of the mass-damper-spring system (Figure 1), we've explored the underdamped case in the previous post. Figure 1. Schematic of the mass-damper-spring system (adapted from Wikimedia

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. Integration is always more difficult than differentiation as the rules for integration