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Coordinate free proofs: centroid of a triangle |
Calculus |
11 min |
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Dot products and angles |
Calculus |
9 min |
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Components of a vector |
Calculus |
5 min |
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Area of a parallelogram |
Calculus |
3 min |
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Determinants |
Calculus |
5 min |
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Volume of a parallelepiped |
Calculus |
3 min |
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Finding area using cross products |
Calculus |
5 min |
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Matrix multiplication practice |
Calculus |
11 min |
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Solve a linear system using matrices |
Calculus |
18 min |
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Equations of planes |
Calculus |
14 min |
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Distance of a point to a plane |
Calculus |
8 min |
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Systems of linear equations |
Calculus |
12 min |
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Parametrized lines and intersections |
Calculus |
9 min |
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Parametric line intersecting a plane |
Calculus |
8 min |
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Differentiating a vector valued function |
Calculus |
14 min |
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Parametric curves: velocity, acceleration, length |
Calculus |
8 min |
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Graphing surfaces |
Calculus |
8 min |
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Level curves |
Calculus |
10 min |
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Level curves and critical points |
Calculus |
8 min |
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Partial derivatives |
Calculus |
5 min |
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Tangent plane approximation |
Calculus |
7 min |
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Least squares |
Calculus |
9 min |
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Second derivative test |
Calculus |
9 min |
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Max/Min |
Calculus |
14 min |
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Total differentials and the chain rule |
Calculus |
12 min |
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Tangent planes |
Calculus |
9 min |
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Gradient and directional derivative |
Calculus |
14 min |
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Lagrange multipliers |
Calculus |
10 min |
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Lagrange multipliers (3 variables) |
Calculus |
13 min |
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The chain rule with constraints |
Calculus |
15 min |
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Gradients – composition |
Calculus |
10 min |
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Regions of integration |
Calculus |
18 min |
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Changing the order of integration |
Calculus |
6 min |
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Integration in polar coordinates |
Calculus |
18 min |
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Integrals with density |
Calculus |
16 min |
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Change of variables |
Calculus |
9 min |
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Integral of exp(-x^2) |
Calculus |
10 min |
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Change of variables |
Calculus |
20 min |
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Line integrals: path dependence |
Calculus |
16 min |
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Line integrals: parametrization independence |
Calculus |
13 min |
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Line integrals by geometric reasoning |
Calculus |
11 min |
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Fundamental theorem of line integrals |
Calculus |
11 min |
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Non-conservative vector fields |
Calculus |
10 min |
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Potentials of gradient fields |
Calculus |
11 min |
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Greens Theorem: an off center circle |
Calculus |
8 min |
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