9 posts tagged with "cat:MathPhysics"

Regardless of discipline, many fields need to be able to process, manipulate, and visualize data. This article introduces the basics of plotting data with Python using Matplotlib. View the notebook on Github or experiment with it yourself on Google Colab.

This is a brief writeup of some of my notes on how to calculate probabilities.

Notation​

$P(A \cap B) \rightarrow$ The probability of A AND B

$P(A \cup B) \rightarrow$ The probability of A OR B

$P(A | B) \rightarrow$ The conditional probability of A given B

This article introduces some of the basic concepts of batteries with particular applications for hobby-level small aircraft projects and similar. My aim for this article is to supplement my students' research for their senior design projects and provide an introductory walkthrough of the topic.

This was an interesting mathematical exploration.

I was messing around with a fun navigation problem the other day and thought I'd share it. I was scrolling through a weather app on my phone when I came across the sunrise and sunset times and wanted to try calculating my longitude from these times.

Most of us know that 32 degrees Fahrenheit is the temperature at which water freezes. We also know that this correlates to 0 degrees Celsius. But for many of us, our knowledge stops there and to convert between the two scales we must resort to either looking it up using some sort of app or calculating it by hand using a formula that in involves multiplying by either nine-fifths of five-ninths and adding or subtracting 32 and we often have to lookup the formula to remember which.

I was first exposed to Newton's Method in my undergraduate numerical methods course. I've used it a number of times since then in undergraduate and graduate courses, but I didn't begin to gain an appreciation for its power until my recent navigation systems course. To take a take a dive into Newton's Method and deepen my understanding of it, I spent a day tinkering with various Newton's Method implementations to solve different type of problems.

One of my homework problems for my modern physics course asked me to calculate the highest velocity of a particle for which the Newtonian approximation of kinetic energy $\frac{1}{2}mv^2$ is accurate to within an error of $0.5\%$ of the actual, relativistic, kinetic energy.

Here, a derivation of the Tsiolkovsky rocket equation from Newton's Second Law is shown. As a disclaimer, this is not original work and is not intended to be. It is shown for reference purposes. In fact multiple derivations of the equation can be found here.