Derivatives: The Movie (A Catalog of Derivation Operators)

In this feature presentation, we go over many elements of the vast theory of derivations that occur within the study of differential geometry, a generalization of calculus itself.

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Time Stamps

0:00 - 1:44 - Intro & Disclaimer
1:45 - 12:15 - Summary of the Operators

Elementary Derivatives:

12:16 - 14:57 - Ordinary Derivatives
15:00 - 18:40 - Partial Derivatives
18:44 - 20:35 - Gradients & Directional Derivatives
20:38 - 21:57 - Divergence & Curl
21:59 - 22:53 - Laplacians
22:54 - 24:33 - d'Alembertians
24:34 - 25:33 - Jacobians & Hessians
25:34 - 27:34 - Holomorphic Derivatives
27:37 - 29:03 - Wirtinger Derivatives

Non-Elementary Derivatives:

29:05 - 30:28 - Laplace-Beltrami Operators
30:29 - 33:03 - Covariant Derivatives
33:04 - 34:41 - Lie Derivatives
34:42 - 44:55 - Exterior Derivatives & Codifferentials
44:57 - 48:31 - Hodge Laplacians & Dolbeault Operators
48:33 - 52:08 - Geometric Derivatives
52:11 - 55:11- Exterior Covariant Derivatives
55:12 - 59:11 - Frechet Derivatives & Gateaux Differentials
59:14 - 1:02:39 - Functional Derivatives & Variations
1:02:42 - 1:11:23 - Dirac Operators
1:11:24 - 1:18:30 - Fueter Operators
1:18:32 - 1:21:13 - Witt Operators & Virasoro Operators

Further Generalizations of Derivation Operators:

1:22:02 - 1:27:30 - Discrete Derivatives & Quantum Derivatives
1:27:32 - 1:31:28 - Fractional Derivatives & Malliavin Derivatives
1:31:30 - 1:35:20 - Hausdorff Fractal Derivatives
1:35:22 - 1:39:12 - Differential Graded Algebras
1:39:13 - 1:41:44 - Quasi-Derivations & Operad Deformations
1:41:45 - 1:53:43 - Derivation Functors & Differential Combinators

[TheLethalDomain]

Time Stamps


0:00 - 1:44 - Intro & Disclaimer
1:45 - 12:15 - Summary of the Operators

Elementary Derivatives:

12:16 - 14:57 - Ordinary Derivatives
15:00 - 18:40 - Partial Derivatives
18:44 - 20:35 - Gradients & Directional Derivatives
20:38 - 21:57 - Divergence & Curl
21:59 - 22:53 - Laplacians
22:54 - 24:33 - d'Alembertians
24:34 - 25:33 - Jacobians & Hessians
25:34 - 27:34 - Holomorphic Derivatives
27:37 - 29:03 - Wirtinger Derivatives

Non-Elementary Derivatives:

29:05 - 30:28 - Laplace-Beltrami Operators
30:29 - 33:03 - Covariant Derivatives
33:04 - 34:41 - Lie Derivatives
34:42 - 44:55 - Exterior Derivatives & Codifferentials
44:57 - 48:31 - Hodge Laplacians & Dolbeault Operators
48:33 - 52:08 - Geometric Derivatives
52:11 - 55:11- Exterior Covariant Derivatives
55:12 - 59:11 - Frechet Derivatives & Gateaux Differentials
59:14 - 1:02:39 - Functional Derivatives & Variations
1:02:42 - 1:11:23 - Dirac Operators
1:11:24 - 1:18:30 - Fueter Operators
1:18:32 - 1:21:13 - Witt Operators & Virasoro Operators

Further Generalizations of Derivation Operators:

1:22:02 - 1:27:30 - Discrete Derivatives & Quantum Derivatives
1:27:32 - 1:31:28 - Fractional Derivatives & Malliavin Derivatives
1:31:30 - 1:35:20 - Hausdorff Fractal Derivatives
1:35:22 - 1:39:12 - Differential Graded Algebras
1:39:13 - 1:41:44 - Quasi-Derivations & Operad Deformations
1:41:45 - 1:53:43 - Derivation Functors & Differential Combinators

[TheoriesofEverything]

What I didn't know I needed. Great job.

[quentonc]

thank u for taking the time to add timestamps & chapters, it helped me pick the subjects that i was more focused on

[yagzkadas]

As a 17 years old teenage I have no idea what is going on but good job.

[cloverisfan]

Can’t wait for the sequel: Integrals and the prequel: Limits

[Flaystray]

Fantastic, but needed examples on each type.

[ZoonCrypticon]

I have never listened to a disclaimer for mathematics. It is I hope not a part of brain cell damage, that will follow.