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Multivariable Calculus | The directional derivative.
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Multivariable Calculus
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- 1 Multivariable Calculus | The notion of a vector and its length.
- 2 Multivariable Calculus | The equation of a sphere.
- 3 Multivariable Calculus | The scalar multiple of a vector.
- 4 Multivariable Calculus | Unit Vectors
- 5 Multivariable Calculus | The dot product.
- 6 Multivariable Calculus | Some applications of the dot product.
- 7 Multivariable Calculus | The projection of a vector.
- 8 Multivariable Calculus | The Cross Product
- 9 Multivariable Calculus | The cross product, area, and volume.
- 10 Multivariable Calculus | Cross Product Examples
- 11 Multivariable Calculus | Three equations for a line.
- 12 Multivariable Calculus | Interactions of lines in 3 dimensions.
- 13 Multivariable Calculus | The Equation of a Plane
- 14 Multivariable Calculus | Interaction of a line and a plane in three dimensions.
- 15 Multivariable Calculus | Some properties of derivatives of vector valued functions.
- 16 Multivariable Calculus | Integrals of vector valued functions.
- 17 Multivariable Calculus | ArcLength
- 18 Multivariable Calculus | ArcLength Example
- 19 Multivariable Calculus | Curvature
- 20 Multivariable Calculus | Curvature Part 2
- 21 Multivariable Calculus | The derivative of a vector valued function.
- 22 Multivariable Calculus | A few examples of curves in 3 dimensions.
- 23 Multivariable Calculus | Three vectors associated to a curve.
- 24 Multivariable Calculus | The Normal and Osculating Planes
- 25 Multivariable Calculus | The domain of a multivariable function.
- 26 Multivariable Calculus | Showing a limit does not exist
- 27 Multivariable Calculus | Finding a limit with polar coordinates.
- 28 Multivariable Calculus | The Squeeze Theorem
- 29 Multivariable Calculus | Definition of partial derivatives.
- 30 Multivariable Calculus | Higher partial derivatives.
- 31 Multivariable Calculus | The tangent plane
- 32 Multivariable Calculus | Finding the equation of a tangent plane.
- 33 Multivariable Calculus | The tangent plane of a level surface.
- 34 Multivariable Calculus | The directional derivative.
- 35 Multivariable Calculus | The gradient and directional derivatives.
- 36 Multivariable Calculus | The second derivative test.
- 37 Multivariable Calculus | The extreme value theorem.
- 38 Multivariable Calculus | Lagrange multipliers
- 39 Multivariable Calculus | Introduction to double integrals
- 40 Multivariable Calculus | Double integrals over rectangular regions.
- 41 Multivariable Calculus | The chain rule.
- 42 Multivariable Calculus | Implicit derivatives with the chain rule.
- 43 Multivariable Calculus | A special double integral.
- 44 Multivariable Calculus | Double integrals over general regions.
- 45 Multivariable Calculus | Double integrals and polar coordinates.
- 46 Multivariable Calculus | Changing the order of integration in double integrals.
- 47 Multivariable Calculus | Triple integrals over a rectangular box.
- 48 Multivariable Calculus | Estimating a double integral.
- 49 Multivariable Calculus | Triple integrals over general regions.
- 50 Multivariable Calculus | Triple integrals with polar coordinates.
- 51 Multivariable Calculus | Triple integrals in spherical coordinates.
- 52 Multivariable Calculus | The volume of a torus.
- 53 Multivariable Calculus | Triple integral with spherical coordinates: Example.
- 54 Multivariable Calculus | Transformations of the plane.
- 55 Multivariable Calculus | The Jacobian
- 56 Multivariable Calculus | Change of variables for multiple integrals.
- 57 Multivariable Calculus | Change of variables for multiple integrals examples.
- 58 Multivariable Calculus | More change of variables in multiple integrals.
- 59 Multivariable Calculus | Definition of line integral with respect to arclength.
- 60 Multivariable Calculus | Scalar line integral examples.
- 61 Multivariable Calculus | What is a vector field.
- 62 Multivariable Calculus | Conservative vector fields.
- 63 Multivariable Calculus | Line integrals with piecewise defined curves.
- 64 Multivariable Calculus | Line integrals over vector fields.
- 65 Multivariable Calculus | Differentiability
- 66 Multivariable Calculus | Differentiable implies continuous.
- 67 Multivariable Calculus | Fundamental Theorem of Line Integrals
- 68 Multivariable Calculus | Line integrals over vector fields -- a few examples.
- 69 Multivariable Calculus | Conservative vector fields and path independence.
- 70 Multivariable Calculus | Green's Theorem
- 71 Multivariable Calculus | Changing the order of integration.
- 72 Multivariable Calculus | Green's Theorem Verification Example 1
- 73 Multivariable Calculus | Green's Theorem verification example 2.
- 74 Multivariable Calculus | Two more Green's theorem examples.
- 75 Multivariable Calculus | Vector forms of Green's Theorem.
- 76 Multivariable Calculus | When Green's theorem doesn't apply and winding numbers.
- 77 Multivariable Calculus | Gradient, Curl, and Divergence
- 78 Multivariable Calculus | Parameterized surfaces
- 79 Multivariable Calculus | The area of a parameterized surface.
- 80 Multivariable Calculus | Surface area of a parameterized surface, example.
- 81 Multivariable Calculus | The orientation of a parametric surface with examples.
- 82 Multivariable Calculus | Stoke's Theorem
- 83 Multivariable Calculus | Verifying Stoke's theorem, example 1.
- 84 Multivariable Calculus | Stoke's theorem verification example 2.
- 85 Multivariable Calculus | The Divergence Theorem
- 86 Multivariable Calculus | Verifying the Divergence Theorem
- 87 Multivariable Calculus | When the divergence theorem doesn't apply.
- 88 Multivariable Calculus | Two Stoke's theorem examples.
- 89 Multivariable Calculus | Divergence Theorem Example
