Welcome back. Today, we will explore a concept that is central to the study of linear partial differential equations: that of the fundamental solution. As its name suggests, a fundamental solution is a very special solution to a PDE that serves as a building block for more general solutions. In this blog, my goal is to derive the fundamental solution to Laplace’s … [Read more...] about The Fundamental Solution of Laplace’s Equation and its Importance in Physics
Articles
Eyewitness Identification – Part 1
Eyewitnesses are one of the most relied upon pieces of evidence in the trial process. Most jury members do not understand the limitations of eyewitness testimony, and they rely upon it as “fact”. Memory doesn’t function like a video camera: it is malleable and can be influenced by a lot of outside factors. Unlike eyewitness testimony, DNA is conclusive. The Innocence Project … [Read more...] about Eyewitness Identification – Part 1
Reviewing Altspace VR: One of the First of its Kind
Nowadays, the elusive term “The Metaverse” isn’t so foreign to most people anymore. It’s the concept of a virtual world in parallel to our actual reality. There are many ways for people to engage with this world- but by far the most immersive is through VR. You’re in the virtual world- a participant, rather than an observer. The most popular Metaverse “worlds” you can visit are … [Read more...] about Reviewing Altspace VR: One of the First of its Kind
The Laplace Transform: A More Powerful Extension of the Fourier Transform
Welcome back. This week, I wanted to discuss the Laplace transform, which is an incredibly useful tool for solving linear ordinary and partial differential equations. The primary reason for its utility is that it converts differential equations in terms of one unknown function into algebraic equations in terms of another unknown function that can be solved relatively quickly. … [Read more...] about The Laplace Transform: A More Powerful Extension of the Fourier Transform
Cognitive-Enhancing Drugs
Nootropics are a category of drugs designed to improve cognitive function, learning, memory, and performance. These drugs are useful for treating ADHD, narcolepsy, or Alzheimer's. While they are most useful for those whose cognition is impaired, “normal” people have begun to look into the use of these “smart drugs” to increase cognitive performance (Medical News Today). … [Read more...] about Cognitive-Enhancing Drugs