Multivariable calculus
4.0
(1)
19 learners
What you'll learn
This course includes
- 24.3 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 129 lessons • 24.3 hours of video
Multivariable calculus
129 lessons
• 17.3 hours
Multivariable calculus
129 lessons
• 17.3 hours
- Derivative of a position vector valued function | Multivariable Calculus | Khan Academy 14:45
- Divergence theorem proof (part 3) | Divergence theorem | Multivariable Calculus | Khan Academy 06:21
- Type I regions in three dimensions | Divergence theorem | Multivariable Calculus | Khan Academy 08:39
- Divergence theorem proof (part 5) | Divergence theorem | Multivariable Calculus | Khan Academy 03:12
- Divergence theorem proof (part 2) | Divergence theorem | Multivariable Calculus | Khan Academy 07:30
- 3D divergence theorem intuition | Divergence theorem | Multivariable Calculus | Khan Academy 09:14
- Divergence theorem example 1 | Divergence theorem | Multivariable Calculus | Khan Academy 10:45
- Type III regions in three dimensions | Divergence theorem | Multivariable Calculus | Khan Academy 06:33
- Divergence theorem proof (part 4) | Divergence theorem | Multivariable Calculus | Khan Academy 08:09
- Type II regions in three dimensions | Divergence theorem | Multivariable Calculus | Khan Academy 07:29
- Divergence theorem proof (part 1) | Divergence theorem | Multivariable Calculus | Khan Academy 08:29
- Introduction to the line integral | Multivariable Calculus | Khan Academy 18:49
- Line integral example 1 | Line integrals and Green's theorem | Multivariable Calculus | Khan Academy 13:03
- Line integral example 2 (part 1) | Multivariable Calculus | Khan Academy 12:53
- Line integral example 2 (part 2) | Multivariable Calculus | Khan Academy 09:58
- Position vector valued functions | Multivariable Calculus | Khan Academy 07:45
- Differential of a vector valued function | Multivariable Calculus | Khan Academy 05:04
- Vector valued function derivative example | Multivariable Calculus | Khan Academy 12:45
- Line integrals and vector fields | Multivariable Calculus | Khan Academy 16:47
- Using a line integral to find the work done by a vector field example | Khan Academy 11:32
- Parametrization of a reverse path | Khan Academy 07:26
- Scalar field line integral independent of path direction | Multivariable Calculus | Khan Academy 16:22
- Vector field line integrals dependent on path direction | Multivariable Calculus | Khan Academy 15:51
- Path independence for line integrals | Multivariable Calculus | Khan Academy 17:14
- Closed curve line integrals of conservative vector fields | Multivariable Calculus | Khan Academy 08:25
- Example of closed line integral of conservative field | Multivariable Calculus | Khan Academy 11:02
- Second example of line integral of conservative vector field | Multivariable Calculus | Khan Academy 10:19
- Green's theorem proof part 1 | Multivariable Calculus | Khan Academy 14:26
- Green's theorem proof (part 2) | Multivariable Calculus | Khan Academy 19:26
- Green's theorem example 1 | Multivariable Calculus | Khan Academy 10:31
- Green's theorem example 2 | Multivariable Calculus | Khan Academy 07:07
- Constructing a unit normal vector to a curve | Multivariable Calculus | Khan Academy 10:08
- 2D divergence theorem | Line integrals and Green's theorem | Multivariable Calculus | Khan Academy 14:43
- Conceptual clarification for 2D divergence theorem | Multivariable Calculus | Khan Academy 09:28
- Multivariable functions | Multivariable calculus | Khan Academy 06:02
- Representing points in 3d | Multivariable calculus | Khan Academy 06:39
- Introduction to 3d graphs | Multivariable calculus | Khan Academy 07:06
- Interpreting graphs with slices | Multivariable calculus | Khan Academy 05:38
- Contour plots | Multivariable calculus | Khan Academy 05:36
- Parametric curves | Multivariable calculus | Khan Academy 05:51
- Parametric surfaces | Multivariable calculus | Khan Academy 06:21
- Vector fields, introduction | Multivariable calculus | Khan Academy 05:05
- Fluid flow and vector fields | Multivariable calculus | Khan Academy 03:35
- 3d vector fields, introduction | Multivariable calculus | Khan Academy 05:10
- 3d vector field example | Multivariable calculus | Khan Academy 04:04
- Transformations, part 1 | Multivariable calculus | Khan Academy 05:16
- Transformations, part 2 | Multivariable calculus | Khan Academy 04:38
- Transformations, part 3 | Multivariable calculus | Khan Academy 03:29
- Partial derivatives, introduction 10:56
- Partial derivatives and graphs 06:54
- Formal definition of partial derivatives 07:58
- Symmetry of second partial derivatives 07:02
- Gradient 05:31
- Gradient and graphs 06:11
- Directional derivative 07:14
- Directional derivative, formal definition 06:39
- Directional derivatives and slope 08:50
- Why the gradient is the direction of steepest ascent 10:32
- Gradient and contour maps 06:17
- Multivariable chain rule 09:33
- Multivariable chain rule intuition 07:47
- Vector form of the multivariable chain rule 05:25
- Multivariable chain rule and directional derivatives 06:41
- More formal treatment of multivariable chain rule 11:55
- Curvature intuition 04:12
- Curvature formula, part 1 06:06
- Curvature formula, part 2 07:06
- Curvature formula, part 3 08:37
- Curvature formula, part 4 08:34
- Curvature formula, part 5 07:46
- Curvature of a helix, part 1 06:28
- Curvature of a helix, part 2 07:19
- Curvature of a cycloid 04:43
- Computing the partial derivative of a vector-valued function 02:18
- Partial derivative of a parametric surface, part 1 09:29
- Partial derivative of a parametric surface, part 2 07:03
- Partial derivatives of vector fields 08:34
- Partial derivatives of vector fields, component by component 07:31
- Divergence intuition, part 1 06:21
- Divergence intuition, part 2 05:28
- Divergence formula, part 1 03:38
- Divergence formula, part 2 06:04
- Divergence example 04:11
- Divergence notation 04:49
- 2d curl intuition 03:54
- 2d curl formula 05:43
- 2d curl example 05:39
- 2d curl nuance 05:00
- Describing rotation in 3d with a vector 06:06
- 3d curl intuition, part 1 05:50
- 3d curl intuition, part 2 08:17
- 3d curl formula, part 1 07:40
- 3d curl formula, part 2 06:12
- 3d curl computation example 05:35
- Laplacian intuition 05:31
- Laplacian computation example 05:21
- Explicit Laplacian formula 04:03
- Harmonic Functions 10:56
- Jacobian prerequisite knowledge 09:22
- Local linearity for a multivariable function 05:23
- The Jacobian matrix 06:22
- Computing a Jacobian matrix 03:53
- The Jacobian Determinant 08:53
- What is a tangent plane 03:20
- Controlling a plane in space 10:40
- Computing a tangent plane 09:41
- Local linearization 09:13
- What do quadratic approximations look like 04:42
- Quadratic approximation formula, part 1 07:09
- Quadratic approximation formula, part 2 09:50
- Quadratic approximation example 12:09
- The Hessian matrix | Multivariable calculus | Khan Academy 06:10
- Expressing a quadratic form with a matrix 08:20
- Vector form of multivariable quadratic approximation 08:35
- Multivariable maxima and minima 08:04
- Saddle points 05:50
- Warm up to the second partial derivative test 11:37
- Second partial derivative test 11:52
- Second partial derivative test intuition 10:43
- Second partial derivative test example, part 1 06:11
- Second partial derivative test example, part 2 07:43
- Constrained optimization introduction 06:29
- Lagrange multipliers, using tangency to solve constrained optimization 08:43
- Finishing the intro lagrange multiplier example 06:39
- Lagrange multiplier example, part 1 07:50
- Lagrange multiplier example, part 2 06:51
- The Lagrangian 12:28
- Meaning of Lagrange multiplier 10:08
- Proof for the meaning of Lagrange multipliers | Multivariable Calculus | Khan Academy 17:19
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