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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
  • 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 |

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