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0:00 Matrix Calculus
1:28 Scalar Calculus
9:03 Emphasis on Linearization
14:23 Gradients
17:23 Geometrically
24:16 Matrix/Vector Product Rule
29:57 Gradients the straightforward but klunky way
30:41 Gradients the sophisticated way
33:42 Example f(x) = (Ax-b)'(Ax-b)
37:41 Gradient Notation
38:28 The Trace
42:50 Linear Functions of Matrices
46:20 Gradients of Functions from Matrices to Scalars
51:20 Vector to Vector Jacobians
54:59 How are Gradients Used
55:48 The Jacobian Matrix, vectors to vectors
1:05:55 A Key Point -- you don't have to write out the matrix elements
1:06:27 relationship to volumes
1:07:55 Matrices to Matrices
1:08:48 Derivatives of Matrix to Matrix Functions

(From Youtube)