vida vakilian - dept of computer & electrical engineering
TRANSCRIPT
![Page 1: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/1.jpg)
Signals and Systems
1
California State University, Bakersfield
Vida Vakilian
Department of Electrical and Computer Engineering, California State University, Bakersfield
Lecture 6 (Vector Analysis)
![Page 2: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/2.jpg)
Signals and Systems
2
California State University, Bakersfield
Gradient in Cylindrical
![Page 3: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/3.jpg)
Signals and Systems
3
California State University, Bakersfield
Gradient in Cylindrical and Spherical
![Page 4: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/4.jpg)
Signals and Systems
4
California State University, Bakersfield
Gradient Properties
![Page 5: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/5.jpg)
Signals and Systems
5
California State University, Bakersfield
![Page 6: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/6.jpg)
Signals and Systems
6
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
![Page 7: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/7.jpg)
Signals and Systems
7
California State University, Bakersfield
Divergence of a Vector Field
![Page 8: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/8.jpg)
Signals and Systems
8
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
![Page 9: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/9.jpg)
Signals and Systems
9
California State University, Bakersfield
Divergence in Cylindrical & Spherical Coordinates
![Page 10: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/10.jpg)
Signals and Systems
10
California State University, Bakersfield
![Page 11: Vida Vakilian - Dept of Computer & Electrical Engineering](https://reader034.vdocuments.us/reader034/viewer/2022050415/6270d41ada5396119a338d28/html5/thumbnails/11.jpg)
Signals and Systems
11
California State University, Bakersfield