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 heat 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
7:03 How Classic Methods (e.g., Laplace) Relate to Modern Problems
9:17 Laplace Transform with respect to Time
15:10 Solving ODE with Forcing: Homogeneous and Particular Solution
19:12 The Particular Solution and Initial Conditions
28:20 The Homogeneous Solution and Boundary Conditions
31:52 The Solution in Frequency and Time Domains
This video shows how to solve Partial Differential Equations (PDEs) with Laplace Transforms. Specifically we solve the heat 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
7:03 How Classic Methods (e.g., Laplace) Relate to Modern Problems
9:17 Laplace Transform with respect to Time
15:10 Solving ODE with Forcing: Homogeneous and Particular Solution
19:12 The Particular Solution and Initial Conditions
28:20 The Homogeneous Solution and Boundary Conditions
31:52 The Solution in Frequency and Time Domains
![Neural Implicit Flow (NIF) [Physics Informed Machine Learning]](https://i.ytimg.com/vi/y-s1oECkbuU/mqdefault.jpg "Neural Implicit Flow (NIF) [Physics Informed Machine Learning]
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:25 Underlying Concept
// 02:32 Example Problem
04:36 Example Application: Turbulent Data Compression
06:23 Example Application: Sparse Sensor Placement
08:09 NIF is Mesh Agnostic
10:30 Results/Benchmark Data
// 11:00 Growing Vortices/ Cool Pictures
11:40 Shape Net Architectures
12:30 Outro")
