Main content

# Derivatives of multivariable functions

Learn

Partial derivatives, introductionGraphical understanding of partial derivativesFormal definition of partial derivativesSymmetry of second partial derivatives

Learn

GradientGradient and graphsGradient and contour mapsDirectional derivativeDirectional derivative, formal definitionDirectional derivatives and slopeWhy the gradient is the direction of steepest ascent

Learn

Introduction to partial derivativesSecond partial derivativesThe gradientDirectional derivatives (introduction)Directional derivatives (going deeper)

Learn

Vector-valued functions introVector-valued functions differentiationDifferential of a vector valued functionVector valued function derivative example

Learn

Multivariable chain ruleMultivariable chain rule intuitionVector form of the multivariable chain ruleMultivariable chain rule and directional derivativesMore formal treatment of multivariable chain rule

Learn

Curvature intuitionCurvature formula, part 1Curvature formula, part 2Curvature formula, part 3Curvature formula, part 4Curvature formula, part 5Curvature of a helix, part 1Curvature of a helix, part 2Curvature of a cycloid

Learn

Computing the partial derivative of a vector-valued functionPartial derivative of a parametric surface, part 1Partial derivative of a parametric surface, part 2Partial derivatives of vector fieldsPartial derivatives of vector fields, component by component

Learn

Derivatives of vector-valued functionsCurvatureMultivariable chain rule, simple versionPartial derivatives of parametric surfaces

Learn

Divergence intuition, part 1Divergence intuition, part 2Divergence formula, part 1Divergence formula, part 2Divergence exampleDivergence notation

Learn

2d curl intuition2d curl formula2d curl example2d curl nuanceDescribing rotation in 3d with a vector3d curl intuition, part 13d curl intuition, part 23d curl formula, part 13d curl formula, part 23d curl computation example

Learn

DivergenceIntuition for divergence formulaCurl warmup, fluid rotation in two dimensionsCurl, fluid rotation in three dimensions

Learn

Laplacian intuitionLaplacian computation exampleExplicit Laplacian formulaHarmonic Functions

Learn

Jacobian prerequisite knowledgeLocal linearity for a multivariable functionThe Jacobian matrixComputing a Jacobian matrixThe Jacobian Determinant

Learn

No videos or articles available in this lesson

Practice