#####
Partial derivatives, introduction

#####
Graphical understanding of partial derivatives

#####
Formal definition of partial derivatives

#####
Symmetry of second partial derivatives

#####
Partial derivatives

#####
Gradient

#####
Gradient and graphs

#####
Gradient and contour maps

#####
Directional derivative

#####
Directional derivative, formal definition

#####
Directional derivatives and slope

#####
Why the gradient is the direction of steepest ascent

#####
Gradient and directional derivatives

#####
Vector-valued functions intro

#####
Vector-valued functions differentiation

#####
Differential of a vector valued function

#####
Vector valued function derivative example

#####
Differentiating parametric curves

#####
Multivariable chain rule

#####
Multivariable chain rule intuition

#####
Vector form of the multivariable chain rule

#####
Multivariable chain rule and directional derivatives

#####
More formal treatment of multivariable chain rule

#####
Multivariable chain rule

#####
Curvature intuition

#####
Curvature formula, part 1

#####
Curvature formula, part 2

#####
Curvature formula, part 3

#####
Curvature formula, part 4

#####
Curvature formula, part 5

#####
Curvature of a helix, part 1

#####
Curvature of a helix, part 2

#####
Curvature of a cycloid

#####
Curvature

#####
Computing the partial derivative of a vector-valued function

#####
Partial derivative of a parametric surface, part 1

#####
Partial derivative of a parametric surface, part 2

#####
Partial derivatives of vector fields

#####
Partial derivatives of vector fields, component by component

#####
Partial derivatives of vector-valued functions

#####
Divergence intuition, part 1

#####
Divergence intuition, part 2

#####
Divergence formula, part 1

#####
Divergence formula, part 2

#####
Divergence example

#####
Divergence notation

#####
Divergence

#####
Curl

#####
2d curl intuition

#####
2d curl formula

#####
2d curl example

#####
2d curl nuance

#####
Describing rotation in 3d with a vector

#####
3d curl intuition, part 1

#####
3d curl intuition, part 2

#####
3d curl formula, part 1

#####
Laplacian

#####
Laplacian intuition

#####
Laplacian computation example

#####
Explicit Laplacian formula

#####
Harmonic Functions

#####
The Jacobian Determinant

#####
Jacobian

#####
Jacobian prerequisite knowledge

#####
Local linearity for a multivariable function

#####
The Jacobian matrix

#####
Computing a Jacobian matrix

#####
Tangent planes and local linearization

#####
What is a tangent plane

#####
Controlling a plane in space

#####
Computing a tangent plane

#####
Local linearization