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Outline
Calculus 3
Plane
A line in E^3 is not uniquely determined by a normal vector
Plane and normal vectors
Cross-section and level curves
Cross-sections
Intersection of surfaces
Intersection of two paraboloids
Cylindrical surface
Limit which does not exist
Partial derivatives
Directional derivative
Linear approximation and tangent plane
The second derivative test
Absolute min and max
Riemann sum in three dimensional space
A double integral over a rectangle
Integration on a y-simple region
Domain of integration in three dimensional space
Spherical coordinates
Parametrized plane curve
Parametrized surface
The tangent vector to a space curve
Another parametrization of the helix
Tangent vectors to a parametrized surface
Tangent plane to a surface of revolution
A 2-dimensional parallelepiped in the 3-dimensional space
A parallelepiped in the three dimensional space
example_1_5
example_3_1
example_3_2
example_3_3
example_4_1
example_4_2
example_4_3
Gradient and level curves
Gradient and level surfaces
2d vector field and two line integrals
3d vector field and a line integral
Max/Min with a constraint
Line integrals over scalar fields
Cross-product
Mobius band
Orientable closed surface
Stokes
Calculus 3
Author:
Daniel Vallieres
Topic:
Calculus
Plane
A line in E^3 is not uniquely determined by a normal vector
Plane and normal vectors
Cross-section and level curves
Cross-sections
Intersection of surfaces
Intersection of two paraboloids
Cylindrical surface
Limit which does not exist
Partial derivatives
Directional derivative
Linear approximation and tangent plane
The second derivative test
Absolute min and max
Riemann sum in three dimensional space
A double integral over a rectangle
Integration on a y-simple region
Domain of integration in three dimensional space
Spherical coordinates
Parametrized plane curve
Parametrized surface
The tangent vector to a space curve
Another parametrization of the helix
Tangent vectors to a parametrized surface
Tangent plane to a surface of revolution
A 2-dimensional parallelepiped in the 3-dimensional space
A parallelepiped in the three dimensional space
example_1_5
example_3_1
example_3_2
example_3_3
example_4_1
example_4_2
example_4_3
Gradient and level curves
Gradient and level surfaces
2d vector field and two line integrals
3d vector field and a line integral
Max/Min with a constraint
Line integrals over scalar fields
Cross-product
Mobius band
Orientable closed surface
Stokes
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