## 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
- Gradient
- Gradient and graphs
- Directional derivative
- Directional derivative, formal definition
- Directional derivatives and slope
- Why the gradient is the direction of steepest ascent
- Gradient and contour maps
- 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
- Quadratic approximation example
- The Hessian matrix
- Expressing a quadratic form with a matrix
- Vector form of multivariable quadratic approximation
- Multivariable maxima and minima
- Saddle points
- 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 |