The Vector Calculus Behind Gradient Descent Explained

We learn together the Equations behind Gradient Descent, and how all the various components enable Machines to Learn through the tools that Multivariable Calculus provides us.

Part 2 where I implement this equation in Python to train a Machine Learning model:
https://youtu.be/FeEUeX0NlDg

Want to learn more about the Gradient?
https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivative #gradient-and-directional-derivatives

3Blue1Brown's excellent explanation of Gradient Descent
https://www.youtube.com/watch?v=IHZwWFHWa-w

Article Form of above link:
https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions/a/what-is-gradient-descent?modal=1

with this video going in depth into the Chain Rule with Backpropagation
https://www.youtube.com/watch?v=tIeHLnjs5U8&t=174s

TIMESTAMPS:
0:00 Motivation
0:47 Examples of Parameters
1:15 Theta Vector
2:03 Gradient Descent Algorithm
4:00 Cost Function
5:17 Derivative of the Cost Function
6:45 Full Gradient Descent
7:44 But We Can Do Better
8:36 The Gradient Vector
9:31 Visual Intuition for the Gradient
10:41 More on the Gradient
11:16 Gradient Field
11:50 Mapping the Gradient Field to a Surface
12:35 Working with the Gradient Vector
13:14 The Directional Derivative
14:11 Visual Intuition for the Directional Derivative
14:40 The Gradient of the Cost Function