The Most Important Math Formula For Understanding Physics
Math is the language of physics, and there's one formula that you'll encounter time and again in your study of physics: the Taylor series. Get the notes for free here: https://courses.physicswithell....iot.com/notes-sign-u
If I had to name one mathematical theorem that's the most essential for understanding physics, it would be Taylor's formula. It shows up in virtually everything we do in physics. In this video, I'll teach you the basics of Taylor series, and show you a few applications in different corners of physics. In the first part, we'll go through the math, including how to write Taylor's formula in a particularly beautiful way that also makes the generalization to the multi-variable case straightforward. In the second half, we'll look at three physics applications. First, we'll discuss how to linearize complicated F = ma equations to simplify them in special limits. Then we'll learn to take the non-relativistic limit of Einstein's energy formula, and see how it's related to the fine-structure correction to the binding energy of a hydrogen atom. And third we'll look at the definition of the momentum operator in quantum mechanics.
All about pendulums: https://youtu.be/0q0L7Fj4dk8
Taylor expanding the potential energy and discovering the harmonic oscillator: https://youtu.be/bmGqhM-tUk4
Dimensional analysis and the binding energy of hydrogen: https://youtu.be/kC6U900CvwY
Defining the momentum operator in quantum mechanics: https://youtu.be/_lz1VfI6Wxk
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About physics help room videos:
These are intro-level physics videos aimed at students taking their first physics classes. In each video, I'll teach you the fundamentals of a particular physics topic you're likely to meet in your first classes on mechanics and electromagnetism.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at https://www.physicswithelliot.com.
