Uploaded February 2023 | Updated September 2026, 2 weeks ago
This video derives Euler's formula (one of the most important formulas in all of mathematics!!!) from the Taylor series of the complex exponential exp(i*theta).
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Euler's formula and the Taylor series of exp(i theta)
10:49 e^(i pi) = -1
13:19 DeMoivre's Formula
This video derives Euler's formula (one of the most important formulas in all of mathematics!!!) from the Taylor series of the complex exponential exp(i*theta).
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Euler's formula and the Taylor series of exp(i theta)
10:49 e^(i pi) = -1
13:19 DeMoivre's Formula
![AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]](https://i.ytimg.com/vi/T4iJ10TAIMg/mqdefault.jpg "AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]
This video discusses the fifth stage of the machine learning process: (5) selecting and implementing an optimization algorithm to train the model. There are opportunities to incorporate physics into this stage of the process, such as using constrained optimization to force a model onto a susbpace or submanifold characterized by a symmetry or other physical constraint.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:45 Case Study: KKT Constrained Least Squares
06:18 Case Study: Physics Informed DMD
14:00 Loss vs Optimization of Subspace Constraints
17:50 Subspace Constraints and Symmetry
19:28 Case Study: Symbolic Regression and Evolutionary Optimization
22:25 Parsimony and Sparse Optimization Algorithms
25:03 Case Study: SINDy and SR3
28:38 Parsimony and Sparsity Hyperparameters
30:55 Outro")
