Give Me 50 min, I'll Make Multivariable Calculus Click Forever

*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 *Social media:* X: https://x.com/ZacharyHuang12 LinkedIn: https://www.linkedin.com/in/zachary-h-23aa37172/ Github: https://github.com/zachary62 Discord: https://discord.com/invite/hUHHE9Sa6T Medium: https://medium.com/@zh2408 Substack: https://zacharyhuang.substack.com/ *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.