Weyl's law and hearing the area of a drum II
(Part II) H. Lorentz in 1910 gave a series of lectures titled "Old and new problems in physics". In the last lecture he mentions that J. Jean is interested in studying the growth rate of overtones of an electromagnetic wave in a bounded domain. He conjectures that the growth rate is independent of the shape of the domain and depends only on the volume and dimension of the domain. Herman Weyl, who was in attendance, precisely describes how fast these overtones grow two years after this lecture series. Since Weyl's law holds for vibrating membranes, we start by describing the overtones of a drumhead via Dirichlet eigenvalues, compute the eigenvalues explicitly for a string with fixed ends, and build towards a proof of Weyl's law in 2D for simply connected domains.
Видео Weyl's law and hearing the area of a drum II канала USF GradMath
Видео Weyl's law and hearing the area of a drum II канала USF GradMath
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
![Weyl's law and hearing the area of a drum](https://i.ytimg.com/vi/HiCA0n6x3Jo/default.jpg)
![The Essentials of Viscosity Solutions in R^n III](https://i.ytimg.com/vi/v3F4kv8f9v8/default.jpg)
![Primes of the form p = x^2 + n*y^2](https://i.ytimg.com/vi/VBPrP4nChbo/default.jpg)
![Martingales and Stopping Times II](https://i.ytimg.com/vi/Y2OvW7mmLso/default.jpg)
![Derivation of Nonlinear Schrödinger Equation From Approximation of Maxwell's Equations](https://i.ytimg.com/vi/9jVp0gKIywU/default.jpg)
![Stochastic Games for PDE](https://i.ytimg.com/vi/TWf_XLzzUPI/default.jpg)
![Introductory Lectures on Quantum Field Theory: Lecture 2](https://i.ytimg.com/vi/nHAaP4UO9kA/default.jpg)
![The Essentials of Viscosity Solutions in R^n](https://i.ytimg.com/vi/0FRNeTc6Xyc/default.jpg)
![Differentiation in real topological vector spaces](https://i.ytimg.com/vi/Tr2NVmJk1A4/default.jpg)
![Asymptotic Methods in Analysis](https://i.ytimg.com/vi/nDw2wLPQv3M/default.jpg)
![A Brief Introduction to Lamplighter Groups and Diestel-Leader Graphs](https://i.ytimg.com/vi/Sl0TZMu7mo0/default.jpg)
![Covid-19 Spreading: An Eigenvalue Viewpoint](https://i.ytimg.com/vi/3EouErwqbtk/default.jpg)
![Martingales and Stopping Times, Part I](https://i.ytimg.com/vi/79dmo6O9PqE/default.jpg)
![Methods of nonlinear equations in the theory of algebraic geometry II](https://i.ytimg.com/vi/uJwxtLwQzUQ/default.jpg)
![Introduction to Matroids](https://i.ytimg.com/vi/SljIEkfzloA/default.jpg)
![Introduction to Probability Theory](https://i.ytimg.com/vi/pUfZzRKuXqM/default.jpg)
![Extremal Graph Theory and the Problem of Zarankiewicz: Part 1](https://i.ytimg.com/vi/OJ4ZehfJY54/default.jpg)
![An Introduction to Coding Theory](https://i.ytimg.com/vi/NULv-dp-UzQ/default.jpg)
![Complex dynamics: Julia set generated from a family of quadratic functions](https://i.ytimg.com/vi/-jF_6nN9ifI/default.jpg)
![A survey of equilibrium in the plane](https://i.ytimg.com/vi/Hye1gkDkCxU/default.jpg)
![Introduction to Probability Theory II](https://i.ytimg.com/vi/BQkheSwlQhw/default.jpg)