Mathematics is the language of physics, and there is a formula that you will encounter time and time again in your study of physics: the Taylor series. Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up

If I had to cite a mathematical theorem essential to understanding physics, it would be Taylor's formula. This shows up in virtually everything we do in physics. In this video I will teach you the basics of the Taylor series and show you some applications in different areas of physics. In part one, we'll review the math, including how to write the Taylor formula in a particularly beautiful way that also makes generalization simple to the multivariable case. In the second half, we will look at three applications in physics. First, we will see how to linearize complicated F = ma equations to simplify them within special limits. Next, we will learn to take the non-relativistic limit of Einstein's energy formula and see how it relates to the fine structure correction of the binding energy of a hydrogen atom. And third, we will look at the definition of the momentum operator in quantum mechanics.

All about pendulums: https://youtu.be/0q0L7Fj4dk8

Taylor expands potential energy and discovers the harmonic oscillator: https://youtu.be/bmGqhM-tUk4

Dimensional analysis and hydrogen bonding energy: https://youtu.be/kC6U900CvwY

Define the momentum operator in quantum mechanics: https://youtu.be/_lz1VfI6Wxk

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About Physics Help Room Videos:
These are introductory physics videos aimed at students taking their first physics courses. In each video, I will teach you the fundamentals of a particular physics topic that you are likely to encounter in your first lessons in mechanics and electromagnetism.

On me:
I'm Dr. Elliot Schneider. I love physics and I also want to help others learn (and love) physics. Whether you are a beginner just starting out in your study of physics, a more advanced student, or a lifelong learner, I hope you find resources here that will deepen your understanding of the laws of nature. For more interesting physics stuff, visit me at https://www.physicswithelliot.com.

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