Applications of Eigenvalues @drpeyam

Uploaded March 2025 | Updated September 2026, 1 week ago

Applications of Eigenvalues

What is an eigenvalue and what are its applications? Here we present the concept of eigenvalues and eigenvectors, which play a crucial role not only in linear algebra, with diagonalization and Markov chains and data science and AI, but also in differential equations, to solve systems of differential equations. We discuss the applications of resonance but also we answer Mar Kac famous question: Can you hear the shape of a drum. Namely eigenvalues have some very neat applications in music and principal harmonics and overtones, which we discuss as well. Enjoy this calculus and linear algebra and music extravaganza

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$Solving the logistic equation Solving the logistic equation. What does the fox say? Here I solve a differential equation using separation of variables and partial fractions and integrals. It models the population of bunnies but with a limited factor. It gives a surprisingly good model approximation of populations like in Belgium. Enjoy this calculus adventure Subscribe to my channel: https://youtube.com/drpeyam TikTok: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$

$Half integral of x Defining the half integral, which is halfway between a function and its integral. Done by analogy with half derivatives, by finding formulas for the derivatives of power functions. It uses the factorial which is then generalized to the gamma function with Gaussian integrals. I also mention trig functions and applications to broken processes. This is a delight for any calculus student or anyone who is interested in fractional derivatives. 0:00 Introduction 0:30 Analogy 2:58 Gamma Function 5:00 Half integral of x 9:37 Properties and Applications Half Derivative: https://youtu.be/gaAhCTDc6oA YT channel: https://youtube.com/drpeyam TikTok channel: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$