## Multivariable calculus

Multivariable calculus

• Multivariable functions | Multivariable calculus |
• Representing points in 3d | Multivariable calculus |
• Introduction to 3d graphs | Multivariable calculus |
• Interpreting graphs with slices | Multivariable calculus |
• Contour plots | Multivariable calculus |
• Parametric curves | Multivariable calculus |
• Parametric surfaces | Multivariable calculus |
• Vector fields, introduction | Multivariable calculus |
• Fluid flow and vector fields | Multivariable calculus |
• 3d vector fields, introduction | Multivariable calculus |
• 3d vector field example | Multivariable calculus |
• Transformations, part 1 | Multivariable calculus |
• Transformations, part 2 | Multivariable calculus |
• Transformations, part 3 | Multivariable calculus |
• Partial derivatives, introduction
• Partial derivatives and graphs
• Formal definition of partial derivatives
• Symmetry of second partial derivatives
• Directional derivative
• Directional derivative, formal definition
• Directional derivatives and slope
• Why the gradient is the direction of steepest ascent
• Position vector valued functions | Multivariable Calculus |
• Derivative of a position vector valued function | Multivariable Calculus |
• Differential of a vector valued function | Multivariable Calculus |
• Vector valued function derivative example | Multivariable Calculus |
• 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
• 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
• 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
• Divergence intuition, part 1
• Divergence intuition, part 2
• Divergence formula, part 1
• Divergence formula, part 2
• Divergence example
• Divergence notation
• 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
• 3d curl formula, part 2
• 3d curl computation example
• Laplacian intuition
• Laplacian computation example
• Explicit Laplacian formula
• Harmonic Functions
• Jacobian prerequisite knowledge
• Local linearity for a multivariable function
• The Jacobian matrix
• Computing a Jacobian matrix
• The Jacobian Determinant
• What is a tangent plane
• Controlling a plane in space
• Computing a tangent plane
• Local linearization
• What do quadratic approximations look like
• Quadratic approximation formula, part 1
• Quadratic approximation formula, part 2
• The Hessian matrix
• Expressing a quadratic form with a matrix
• Vector form of multivariable quadratic approximation
• Multivariable maxima and minima
• Warm up to the second partial derivative test
• Second partial derivative test
• Second partial derivative test intuition
• Second partial derivative test example, part 1
• Second partial derivative test example, part 2
• Constrained optimization introduction
• Lagrange multipliers, using tangency to solve constrained optimization
• Finishing the intro lagrange multiplier example
• Lagrange multiplier example, part 1
• Lagrange multiplier example, part 2
• The Lagrangian
• Meaning of Lagrange multiplier
• Proof for the meaning of Lagrange multipliers | Multivariable Calculus |
• Introduction to the line integral | Multivariable Calculus |
• Line integral example 1 | Line integrals and Green’s theorem | Multivariable Calculus |
• Line integral example 2 (part 1) | Multivariable Calculus |
• Line integral example 2 (part 2) | Multivariable Calculus |
• Line integrals and vector fields | Multivariable Calculus |
• Using a line integral to find the work done by a vector field example |
• Parametrization of a reverse path |
• Scalar field line integral independent of path direction | Multivariable Calculus |
• Vector field line integrals dependent on path direction | Multivariable Calculus |
• Path independence for line integrals | Multivariable Calculus |
• Closed curve line integrals of conservative vector fields | Multivariable Calculus |
• Example of closed line integral of conservative field | Multivariable Calculus |
• Second example of line integral of conservative vector field | Multivariable Calculus |
• Double integral 1 | Double and triple integrals | Multivariable Calculus |
• Double integrals 2 | Double and triple integrals | Multivariable Calculus |
• Double integrals 3 | Double and triple integrals | Multivariable Calculus |
• Double integrals 4 | Double and triple integrals | Multivariable Calculus |
• Double integrals 5 | Double and triple integrals | Multivariable Calculus |
• Double integrals 6 | Double and triple integrals | Multivariable Calculus |
• Triple integrals 1 | Double and triple integrals | Multivariable Calculus |
• Triple integrals 2 | Double and triple integrals | Multivariable Calculus |
• Triple integrals 3 | Double and triple integrals | Multivariable Calculus |
• Introduction to parametrizing a surface with two parameters | Multivariable Calculus |
• Determining a position vector-valued function for a parametrization of two parameters |
• Partial derivatives of vector-valued functions | Multivariable Calculus |
• Introduction to the surface integral | Multivariable Calculus |
• Example of calculating a surface integral part 1 | Multivariable Calculus |
• Example of calculating a surface integral part 2 | Multivariable Calculus |
• Example of calculating a surface integral part 3 | Multivariable Calculus |
• Surface integral example part 1: Parameterizing the unit sphere |
• Surface integral example part 2: Calculating the surface differential |
• Surface integral example part 3: The home stretch | Multivariable Calculus |
• Surface integral ex2 part 1: Parameterizing the surface | Multivariable Calculus |
• Surface integral ex2 part 2: Evaluating integral | Multivariable Calculus |
• Surface integral ex3 part 1: Parameterizing the outside surface |
• Surface integral ex3 part 2: Evaluating the outside surface | Multivariable Calculus |
• Surface integral ex3 part 3: Top surface | Multivariable Calculus |
• Surface integral ex3 part 4: Home stretch | Multivariable Calculus |
• Conceptual understanding of flux in three dimensions | Multivariable Calculus |
• Constructing a unit normal vector to a surface | Multivariable Calculus |
• Vector representation of a surface integral | Multivariable Calculus |
• Green’s theorem proof part 1 | Multivariable Calculus |
• Green’s theorem proof (part 2) | Multivariable Calculus |
• Green’s theorem example 1 | Multivariable Calculus |
• Green’s theorem example 2 | Multivariable Calculus |
• Constructing a unit normal vector to a curve | Multivariable Calculus |
• 2D divergence theorem | Line integrals and Green’s theorem | Multivariable Calculus |
• Conceptual clarification for 2D divergence theorem | Multivariable Calculus |
• Stokes’ theorem intuition | Multivariable Calculus |
• Green’s and Stokes’ theorem relationship | Multivariable Calculus |
• Orienting boundary with surface | Multivariable Calculus |
• Orientation and stokes | Multivariable Calculus |
• Conditions for stokes theorem | Multivariable Calculus |
• Stokes example part 1 | Multivariable Calculus |
• Stokes example part 2: Parameterizing the surface | Multivariable Calculus |
• Stokes example part 3: Surface to double integral | Multivariable Calculus |
• Stokes example part 4: Curl and final answer | Multivariable Calculus |
• Evaluating line integral directly – part 1 | Multivariable Calculus |
• Evaluating line integral directly – part 2 | Multivariable Calculus |
• 3D divergence theorem intuition | Divergence theorem | Multivariable Calculus |
• Divergence theorem example 1 | Divergence theorem | Multivariable Calculus |
• Stokes’ theorem proof part 1 | Multivariable Calculus |
• Stokes’ theorem proof part 2 | Multivariable Calculus |
• Stokes’ theorem proof part 3 | Multivariable Calculus |
• Stokes’ theorem proof part 4 | Multivariable Calculus |
• Stokes’ theorem proof part 5 | Multivariable Calculus |
• Stokes’ theorem proof part 6 | Multivariable Calculus |
• Stokes’ theorem proof part 7 | Multivariable Calculus |
• Type I regions in three dimensions | Divergence theorem | Multivariable Calculus |
• Type II regions in three dimensions | Divergence theorem | Multivariable Calculus |
• Type III regions in three dimensions | Divergence theorem | Multivariable Calculus |
• Divergence theorem proof (part 1) | Divergence theorem | Multivariable Calculus |
• Divergence theorem proof (part 2) | Divergence theorem | Multivariable Calculus |
• Divergence theorem proof (part 3) | Divergence theorem | Multivariable Calculus |
• Divergence theorem proof (part 4) | Divergence theorem | Multivariable Calculus |
• Divergence theorem proof (part 5) | Divergence theorem | Multivariable Calculus |