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Calculus III
Contents
3 Dimensional space
Cylindrical coordinates
Spherical coordinates
Quadratic surfaces
Two variables functions
3D coordinate system
2D equations in 3D space
Equation of a line in 3D space
Equation of a plane in 3D space
Partial derivatives
Changing one of the variables
Higher order partial derivatives
Differentials & chain rule
Tangent planes
Directional derivatives
Relative extrema & saddle points
Absolute extrema
Lagrange multipliers
Multiple integrals
D. integrals over a rectangle
D. integrals over general regions
D. integrals in polar coordinates
T. integrals in cartesian system
T. integrals in cylinder coordinates
T. integrals in sphe. coordinates
Jacobian & change of variables
Surface area element
Using surface area
Vector Functions
Definitions & graphs
Limits of vector functions
Special unit vectors
Tangent & normal vectors
Arc length of a vect. func.
Curvature of a curve
Velocity & acceleration
Line integrals
Vector fields
Line integrals ds
Line integrals dxdydz
Line integrals of vector fields
Fund. theo. of line integrals
Regions & paths
Conservative vector fields
Green's theorem
Surface integrals
Parametric surfaces
Surface integrals
Surface integrals of vector fields
Stokes' theorem
Divergence theorem
Vector operators
Vector operator Definitions
Applications Curl & divergence
Applications
Cycloid
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