Gradients: A Visual Journey from Baby to Vector
we dive deep into the concept of gradients—one of the most important tools in multivariable calculus and machine learning.
✅ What you’ll learn:
0:00 What a gradient really is: a vector of partial derivatives or the derivative w.r.t. a vector.
0:55 The Baby Gradient: One Variable, One Slope
1:43 From Slope to Gradient Vector
3:20 The Gradient, Explained with Vector Calculus
4:45 Which Way is Uphill Ask the Gradient 3D
5:42 √5?! What Gradient Size REALLY Means!
7:22 Why Is Gradient ALWAYS 90° to Contours?
8:17 Math Proof: Gradient ⊥ Contour Line
9:15 Gradient=Fastest Increase Here’s Why!
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All animations in this video were made with ManimGL and ManimCE, an open-source animation library built in Python. You can find more information about the project here: https://github.com/3b1b/manim, https://github.com/manimCommunity/manim
manimCE: https://www.manim.community/
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