Uploaded January 2023 | Updated September 2026, 2 weeks ago
This video shows how to solve Partial Differential Equations (PDEs) with Laplace Transforms. Specifically we solve the wave equation on a semi-infinite domain.
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview and Problem Setup (Initial Conditions and Boundary Conditions)
3:46 Laplace Transform in Time: PDE to ODE
8:20 Solving the ODE in Space
12:57 General Solution of the Wave Equation
15:38 The Heaviside Function
19:36 Illustration and Method of Characteristics
This video shows how to solve Partial Differential Equations (PDEs) with Laplace Transforms. Specifically we solve the wave equation on a semi-infinite domain.
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview and Problem Setup (Initial Conditions and Boundary Conditions)
3:46 Laplace Transform in Time: PDE to ODE
8:20 Solving the ODE in Space
12:57 General Solution of the Wave Equation
15:38 The Heaviside Function
19:36 Illustration and Method of Characteristics
![Neural ODEs (NODEs) [Physics Informed Machine Learning]](https://i.ytimg.com/vi/nJphsM4obOk/mqdefault.jpg "Neural ODEs (NODEs) [Physics Informed Machine Learning]
This video describes Neural ODEs, a powerful machine learning approach to learn ODEs from data.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
02:09 Background: ResNet
05:05 From ResNet to ODE
07:59 ODE Essential Insight/ Why ODE outperforms ResNet
// 09:05 ODE Essential Insight Rephrase 1
// 09:54 ODE Essential Insight Rephrase 2
11:11 ODE Performance vs ResNet Performance
12:52 ODE extension: HNNs
14:03 ODE extension: LNNs
14:45 ODE algorithm overview/ ODEs and Adjoint Calculation
22:24 Outro")
