Scalar fields and vector functions
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Differentiation of scalar and vector products.
Suppose [Equation goes here - download the original to see it.] is a vector field The functions [Equation goes here - download the original to see it.] are its Cartesian coordinates this function. Then the vector field can be differentiated according to the obvious rule. [Equation goes here - download the original to see it.] Then differentiation of scalar and vector (cross) products of vectors follows the normal product (Leibniz) rule. [Equation goes here - download the original to see it.] We will prove the result for the cross product. That is [Equation goes here - download the original to see it.] Let [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] However the right-hand side of (*) is [Equation 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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