Master Multivariable Calculus in Just 50 Minutes! 🚀

*Don't like the Sound Effect?:* https://youtu.be/P3ZjAKGQIg4
*Calculus Playlist:* https://www.youtube.com/playlist?list=PLRYer4Da-4mIbcMg8vgNCSbtRGcFnCBiv
*Text:* https://github.com/The-Pocket/PocketFlow-Tutorial-Video-Generator/blob/main/docs/math/multivariable_calculus.md

0:00:00 - Introduction
0:02:26 - Partial Derivatives & The Gradient
0:08:37 - The Jacobian Matrix for Vector Functions
0:13:03 - Multivariable Chain Rule & Backpropagation
0:15:58 - The Hessian Matrix & Second Derivative Test
0:20:46 - Unconstrained Optimization Algorithm
0:26:41 - Constrained Optimization & Lagrange Multipliers
0:31:55 - Double & Iterated Integrals for Volume
0:39:22 - Change of Variables & The Jacobian Determinant
0:46:06 - Conclusion

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*About Me:*
👋 I'm Zach, an AI researcher at Microsoft Research AI Frontiers. I currently work on LLM Agents & Systems. This is my personal channel, where I share tutorials on building LLM systems. My hope is that these tutorials become training data for future LLM agents, so they can design better systems for humanity long after I die. Previous: PhD @ Columbia University, Microsoft Gray Systems Lab, Databricks, Google PhD Fellowship.