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Multivariable functions | Multivariable calculus | Khan Academy

Multivariable functions | Multivariable calculus | Khan Academy

Representing points in 3d | Multivariable calculus | Khan Academy

Representing points in 3d | Multivariable calculus | Khan Academy

Introduction to 3d graphs | Multivariable calculus | Khan Academy

Introduction to 3d graphs | Multivariable calculus | Khan Academy

Interpreting graphs with slices | Multivariable calculus | Khan Academy

Interpreting graphs with slices | Multivariable calculus | Khan Academy

Contour plots | Multivariable calculus | Khan Academy

Contour plots | Multivariable calculus | Khan Academy

Parametric curves | Multivariable calculus | Khan Academy

Parametric curves | Multivariable calculus | Khan Academy

Parametric surfaces | Multivariable calculus | Khan Academy

Parametric surfaces | Multivariable calculus | Khan Academy

Vector fields, introduction | Multivariable calculus | Khan Academy

Vector fields, introduction | Multivariable calculus | Khan Academy

Fluid flow and vector fields | Multivariable calculus | Khan Academy

Fluid flow and vector fields | Multivariable calculus | Khan Academy

3d vector fields, introduction | Multivariable calculus | Khan Academy

3d vector fields, introduction | Multivariable calculus | Khan Academy

3d vector field example | Multivariable calculus | Khan Academy

3d vector field example | Multivariable calculus | Khan Academy

Transformations, part 1 | Multivariable calculus | Khan Academy

Transformations, part 1 | Multivariable calculus | Khan Academy

Transformations, part 2 | Multivariable calculus | Khan Academy

Transformations, part 2 | Multivariable calculus | Khan Academy

Transformations, part 3 | Multivariable calculus | Khan Academy

Transformations, part 3 | Multivariable calculus | Khan Academy

Partial derivatives, introduction

Partial derivatives, introduction

Partial derivatives and graphs

Partial derivatives and graphs

Formal definition of partial derivatives

Formal definition of partial derivatives

Symmetry of second partial derivatives

Symmetry of second partial derivatives

Gradient

Gradient and graphs

Gradient and graphs

Directional derivative

Directional derivative

Directional derivative, formal definition

Directional derivative, formal definition

Directional derivatives and slope

Directional derivatives and slope

Why the gradient is the direction of steepest ascent

Why the gradient is the direction of steepest ascent

Gradient and contour maps

Gradient and contour maps

Position vector valued functions | Multivariable Calculus | Khan Academy

Position vector valued functions | Multivariable Calculus | Khan Academy

Derivative of a position vector valued function | Multivariable Calculus | Khan Academy

Derivative of a position vector valued function | Multivariable Calculus | Khan Academy

Differential of a vector valued function | Multivariable Calculus | Khan Academy

Differential of a vector valued function | Multivariable Calculus | Khan Academy

Vector valued function derivative example | Multivariable Calculus | Khan Academy

Vector valued function derivative example | Multivariable Calculus | Khan Academy

Multivariable chain rule

Multivariable chain rule

Multivariable chain rule intuition

Multivariable chain rule intuition

Vector form of the multivariable chain rule

Vector form of the multivariable chain rule

Multivariable chain rule and directional derivatives

Multivariable chain rule and directional derivatives

More formal treatment of multivariable chain rule

More formal treatment of multivariable chain rule

Curvature intuition

Curvature intuition

Curvature formula, part 1

Curvature formula, part 1

Curvature formula, part 2

Curvature formula, part 2

Curvature formula, part 3

Curvature formula, part 3

Curvature formula, part 4

Curvature formula, part 4

Curvature formula, part 5

Curvature formula, part 5

Curvature of a helix, part 1

Curvature of a helix, part 1

Curvature of a helix, part 2

Curvature of a helix, part 2

Curvature of a cycloid

Curvature of a cycloid

Computing the partial derivative of a vector-valued function

Computing the partial derivative of a vector-valued function

Partial derivative of a parametric surface, part 1

Partial derivative of a parametric surface, part 1

Partial derivative of a parametric surface, part 2

Partial derivative of a parametric surface, part 2

Partial derivatives of vector fields

Partial derivatives of vector fields

Partial derivatives of vector fields, component by component

Partial derivatives of vector fields, component by component

Divergence intuition, part 1

Divergence intuition, part 1

Divergence intuition, part 2

Divergence intuition, part 2

Divergence formula, part 1

Divergence formula, part 1

Divergence formula, part 2

Divergence formula, part 2

Divergence example

Divergence example

Divergence notation

Divergence notation

2d curl intuition

2d curl intuition

2d curl formula

2d curl formula

2d curl example

2d curl example

2d curl nuance

Describing rotation in 3d with a vector

Describing rotation in 3d with a vector

3d curl intuition, part 1

3d curl intuition, part 1

3d curl intuition, part 2

3d curl intuition, part 2

3d curl formula, part 1

3d curl formula, part 1

3d curl formula, part 2

3d curl formula, part 2

3d curl computation example

3d curl computation example

Laplacian intuition

Laplacian intuition

Laplacian computation example

Laplacian computation example

Explicit Laplacian formula

Explicit Laplacian formula

Harmonic Functions

Harmonic Functions

Jacobian prerequisite knowledge

Jacobian prerequisite knowledge

Local linearity for a multivariable function

Local linearity for a multivariable function

The Jacobian matrix

The Jacobian matrix

Computing a Jacobian matrix

Computing a Jacobian matrix

The Jacobian Determinant

The Jacobian Determinant

What is a tangent plane

What is a tangent plane

Controlling a plane in space

Controlling a plane in space

Computing a tangent plane

Computing a tangent plane

Local linearization

Local linearization

What do quadratic approximations look like

What do quadratic approximations look like

Quadratic approximation formula, part 1

Quadratic approximation formula, part 1

Quadratic approximation formula, part 2

Quadratic approximation formula, part 2

Quadratic approximation example

Quadratic approximation example

The Hessian matrix | Multivariable calculus | Khan Academy

The Hessian matrix | Multivariable calculus | Khan Academy

Expressing a quadratic form with a matrix

Expressing a quadratic form with a matrix

Vector form of multivariable quadratic approximation

Vector form of multivariable quadratic approximation

Multivariable maxima and minima

Multivariable maxima and minima

Saddle points

Warm up to the second partial derivative test

Warm up to the second partial derivative test

Second partial derivative test

Second partial derivative test

Second partial derivative test intuition

Second partial derivative test intuition

Second partial derivative test example, part 1

Second partial derivative test example, part 1

Second partial derivative test example, part 2

Second partial derivative test example, part 2

Constrained optimization introduction

Constrained optimization introduction

Lagrange multipliers, using tangency to solve constrained optimization

Lagrange multipliers, using tangency to solve constrained optimization

Finishing the intro lagrange multiplier example

Finishing the intro lagrange multiplier example

Lagrange multiplier example, part 1

Lagrange multiplier example, part 1

Lagrange multiplier example, part 2

Lagrange multiplier example, part 2

The Lagrangian

Meaning of Lagrange multiplier

Meaning of Lagrange multiplier

Proof for the meaning of Lagrange multipliers | Multivariable Calculus | Khan Academy

Proof for the meaning of Lagrange multipliers | Multivariable Calculus | Khan Academy

Introduction to the line integral | Multivariable Calculus | Khan Academy

Introduction to the line integral | Multivariable Calculus | Khan Academy