I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. There is no obvious way to integrate the secant function, sec(x). One way is to use

A little while ago, I posted a solution to deriving the reduction formula for the integral of tann(x), that is, integer powers of the tangent function. We use the principles discussed in this post to find

In this video, we perform the integral of 3x2+8 / x3+4x with the f'(x)/f(x) rule... We do this first by expressing the function as a quotient of 2 functions: And realising that q'(x) = 3x^2 + 4, which

In my previous post, I stated that all real world free oscillating systems are damped because their vibrations eventually attenuate away, due to energy dissipation to the surrounding environment. However,

An undamped mass-spring system shown in Figure 1 below. These systems are commonly studied in mechanical engineering and mathematics. They are purely theoretical because they neglect damping forces. A

Continuing our second-order differential equations journey, let's have a look at some possible solutions to the homogeneous second order linear ODE... Now, to recap, the characteristic equation corresponding

In the last post, said I would show you how solutions of second-order linear, differential equations behave physically. But before we can do that, I have to cover this rather dry, math intense proof, in

Let's take a dive into the fascinating world of Second Order Differential equations. These have very important applications in engineering, and you'll see them repeatedly in the modelling of electrical

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 applying De Moivre's Theorem to find the n-th roots of a

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. If we were to try and evaluate powers of complex numbers in their cartesian form,

1. A large pigeon coop in Batman Park, Melbourne, designed to encourage nesting and removal of fertilised eggs.Image source: Wikimedia Commons Previously with our pigeon overpopulation problem, we have

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. This video demonstrates how to calculate monthly loan repayments and time required

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. The product to sum formulas are another subset of trigonometric identities. In this

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 use the results from the previous video to derive the formulas:

Let's recap... Before we look further into the city feral pigeon problem, let's revise what we've established so far with the Leslie model for population growth. Figure 1. Feral pigeons in Catalunya Square,

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain. This video demonstrates just one of the geometric methods you can use to derive the

We've seen in applied mathematics, there are several models for population growth of a species. In my own posts, I have briefly covered the natural (or exponential), logistic growth and predator-prey models.

Suppose you are able to shoot a ball vertically straight up in the air and observe its motion (I don't know why... you might have a ballistic canon installed in the ground that allows you to do such a

Let's take a peek into a more advanced area of study in the field of differential equations. A few days ago @mathowl posted a fascinating article: "The mathematics behind medieval battles" and

Figure 1. Solutions of Equation (10) Let's briefly recap the exponential decay model, which is typically modeled by... Being a separable first order differential equation, we can separate the variables