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Signals and Systems
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California State University, Bakersfield
Vida Vakilian
Department of Electrical and Computer Engineering, California State University, Bakersfield
Lecture 6 (Vector Analysis)
Signals and Systems
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California State University, Bakersfield
Gradient in Cylindrical
Signals and Systems
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California State University, Bakersfield
Gradient in Cylindrical and Spherical
Signals and Systems
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California State University, Bakersfield
Gradient Properties
Signals and Systems
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California State University, Bakersfield
Signals and Systems
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California State University, Bakersfield
Divergence Ø Applies on vectors and results in a scalar quantity.
Ø The divergence denotes the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
Ø For example, consider air as it is heated or cooled. The relevant vector field for this example is the velocity of the moving air at a point. If air is heated in a region it will expand in all directions such that the velocity field points outward from that region.
Ø Therefore the divergence of the velocity field in that region would have a positive value, as the region is a source. If the air cools and contracts, the divergence is negative and the region is called a sink.
Example from Wikipedia
Signals and Systems
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California State University, Bakersfield
Divergence of a Vector Field
Signals and Systems
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California State University, Bakersfield
Divergence Theorem
Useful tool for converting integration over a volume to one over the surface enclosing that volume, and vice versa
Signals and Systems
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California State University, Bakersfield
Divergence in Cylindrical & Spherical Coordinates
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California State University, Bakersfield
Signals and Systems
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California State University, Bakersfield
