u/Ki-Chao

Hello,

I recently put together a short video essay exploring the mathematical transition from standard calculus (which relies on smooth, predictable curves) to the robust algebraic approach required for discontinuous events.

Key concepts covered:

• Why traditional derivatives fail when real systems feature sudden surges.
• Using step functions to synthesize complex architectural wave shapes from scratch.
• Reverse-engineering infinite periodic sequences (like clock pulses) from the s-domain using geometric series.
• The relationship between the Heaviside step function and the Dirac Delta.
• Predicting catastrophic system resonance when damping is removed.

Let me know what you think of the visualizations!

Hey everyone!

I created a short, highly-visual video exploring the mathematical foundations of probability. If you are currently struggling with these topics, I hope this makes the concepts "click" for you!

Here is what the video covers visually:

• What a Random Variable Actually Is
• Probability Mass Function (PMF)
• Cumulative Distribution Function (CDF)
• Some Classical Discrete Models
• Independence & Identical Distributions

I'd love to get your feedback!

Hey everyone,

If you are currently taking Differential Equations or an engineering systems class, you know that solving them in the traditional time domain can be a nightmare (guessing forms for homogeneous/particular solutions, substituting boundary conditions at the end, etc.).

I put together a video breaking down the Laplace Transform and why it's arguably the most powerful tool in classical engineering. Instead of memorizing fragmented processes, the video covers:

Transforming the Equation: Using the integral "convergence squeezer" to move from the time domain to the frequency domain (s-domain).

The Dictionary: How to use standard tables and operational theorems.

Solving the Algebra: Bypassing calculus entirely and handling initial conditions right from the start.

The Inverse Transform: Walking backwards through the portal using partial fraction decomposition (including the Heaviside cover-up method and completing the square for quadratics).

I also walk through a classic damped harmonic oscillator and simultaneous coupled differential equations to show the workflow in action.

If you need a refresher or are learning this for the first time, I hope this helps it click for you! Let me know if you have any questions or if there's a specific math/engineering topic you'd like to see covered next!

Hey Reddit!

I just made an animated video exploring why the human brain is naturally so terrible at grasping probability and how to correct it.

If you've ever been baffled by the "Birthday Paradox" (where a room of just 23 people gives you a >50% chance of a shared birthday), it comes down to how our brains struggle with scale and overcounting.

In this video, I dive into the math and logic behind uncertainty and break it down. I put a lot of work into the visual storytelling to make these complex mathematical rules easy to digest. Whether you're learning statistics or just want to stop getting fooled by randomness, I think you'll find this helpful.

I'd love to hear your thoughts and am happy to answer any questions about the math in the comments!