Scalar fields and vector functions
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Vector calculus - Vector Field
A vector field is a mapping (function) from one vector space to another. For example, suppose we represent an ocean as a two-dimensional disk and the direction and magnitude of the current on the surface of the ocean by a two dimensional vector, then the function that assigns to each point on the surface of the ocean its current vector is a vector field. [Diagram goes here - download the original to see it.] This is the vector field [Equation goes here - download the original to see it.] The functions phi 1 and phi 2 are the components of the vector field and are themselves two-dimensional scalar fields. [Diagram goes here - download the original to see it.] We can represent the rector to which the point [Equation goes here - download the original to see it.] is mapped by a row or column matrix, or by using [Equation goes here - download the original to see it.] notation. [Equation goes here - download the original to see it. [Diagram goes here - download the original to see it.]
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Contents of
Scalar fields and vector functions
1 Vector calculus - Scalar Field
2 Vector calculus - Contour curves
3 Vector calculus - Vector Field
4 Vector calculus - Vector field lines
5 Differentiation of scalar and vector products.
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