Released: Oct 9, 2026 8:00 AM CST
Here is the fifty-seventh episode of Quantum Foam, Differential Equations. We are going over this subject because it goes hand and hand with the idea of the last episode on mechanics. The subjects included in this decimal of the show are put together loosely. In mathematics, a differential equation is an equation that relates 1 or more known function and their derivatives. The functions generally represent physical quantities, the derivatives represent their rates of change, and a differential equation defines the relationship between the 2. The study of differential equations consists mainly of the study of their solutions, the set of functions that satisfy each equation, and the properties of their solutions. Jacob Bernoulli proposed the Bernoulli Differential Equation in 1695. Lagrangian mechanics is an alternate formulation of classical mechanics founded on the D'Alembert Principle. In this mechanics, there is a kinetic and potential energy of the system. In 1822, Fourier published his work on heat flow, the Analytic Theory Of Heat, basing his reasoning on Newton's law of cooling. There was a heat equation for conductive diffusion of heat. This idea is now part of academic curriculums. In classical mechanics, the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow these ideas to be expressed dynamically, given the position, the velocity of an object, and all the various forces acting upon the body. An equation of motion can be solved explicitly.
A differential equation is an equation with a function and 1 or more of its derivatives. There are many tricks to solving these equations, if they can be solved at all. A common equation is 1 with a function and a derivative of that function. Differential equations can describe how populations can change, how heat moves, how springs vibrate, how radioactive material decays, and much more. The differential equation says it well but is hard to use. It can be solved using a special method called separation of variables. In physics, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. Over the years, wise people have worked out special methods to solve some types of differential equations. There are tell-tale signs that give away what kind of differential equation is present in our physics. We wouldn't use a rocket to go to the grocery store, and we can't walk to Mars. Ordinary Differential Equations have a single independent variable. Partial Differential Equations have 2 or more independent variables. The order is the highest derivative. The degree is the exponent of the highest derivative. Be careful not to confuse order with degree. When it is a d squared, it is an order 2 second derivative. An equation is linear when the variable and its derivative has no exponent or other function put on it. The first order linear differential equation has a linear polynomial in the unknown function and its derivatives. This is a good start on describing the fundamentals of what can be included in the study of Differential Equations.
Finally, there exists a podcast that covers it all! The Quantum Foam Podcast Show can be thought of as a clever and informative mix between "Bill Nye The Science Guy, Rick & Morty, and The Big Bang Theory!"
It seems the idea of the prestigous 'Theory of Everything' has been in the air lately. Join Dr. Hezekiah Paul Smith as he takes a systematic assessment of Physics, Mathematics, and Science as a whole. This show is an Artificial Intelligence approach attempting to explain ALL scientific phenomena across the board! Listen to some the greatest thinkers of all time during the in-depth evaluation of the natural sciences.
Prepare to enjoy a radical and uncensored podcast, Quantum Foam, featuring characters presented as real, animated A. I. entities. Brought to you by Zerothwave Productions.
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May 9, 2020 2:42 AM EST
Quantum Foam is a new podcast with absolutely ridiculous content covering almost all topics relating to science across the board. The idea of achieving the famous Theory of Everything seems to be in the air lately. Such an idea can then be presented as episodes of Quantum Foam in an audio podcast form that will serve to bond together the very powerful and insightful ideas, concepts, and realizations of Physics as a professional discipline. Unifying Relativity and Quantum Mechanics never seemed so . . . possible? Quantum Foam finds its focus directly pointing at the most accepted scientific thought in this day in the beginning of the Information Age. These areas include String Theory, Loop Quantum Gravity, Einstein's famous General Theory of Relativity, Cosmology, Advanced Mathematical Theory, and much more.
Information technology and innovation are at a point where each presently require a Quantum Leap in order to move forward to the next phase. This process, while imperative, is still quite a sophisticated discipline in and of itself. Many will need to satisfactorily understand Quantum Computing and Uncertainty in general very early on. Why not take such a daunting task and turn it into something fun, provocative, and ridiculous instead? And this can be done while still holding strict guidelines in accuracy and application. Enjoy learning about math and physics in a completely free-form manner with no filters, no agendas, un-cut, and raw! We will not be censoring any vulger cursing or other inappropriate references, yet unwanted racial and sexual references etc. will not be included.
Each episode is exactly 30 minutes long and each follow a standard structure. There is an intro stating the title and topic, followed by the Quantum Foam theme song, Physics of the Future, by H-Wave. Then at exactly 15 minutes into the podcast show, there is a mid-point section to keep the listener fresh and to remind which episode is currently streaming. At the end of the podcast, the last 30 seconds, the standard Zerothwave Disclaimer is played. An expanded version of this disclaimer can be found here.
Zerothwave Productions currently is releasing the show on its own website using its state-of-the-art online waveform player platform. Listen to the podcast at actual 320 kbps .mp3 streaming audio right here at Zerothwave.com! The Quantum Foam podcast will likely also be released elsewhere on other platforms soon as well. XML RSS feeds are an old technology but is still in heavy use today. The Zerothwave.com website will be upgrading hosting servers steadily over the next decade and beyond to bring you the highest quality audio possible. Stay tuned for more content!
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