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Applied Mathematical Methods by Bhaskar Dasgupta

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18

Scalar and Vector Fields

In the description and analysis of curves and surfaces, as in the previous chapter, points or position vectors are considered as functions of other parameters. In the present chapter, we deal with functions for which space is not the destination, but the domain; i.e. functions which are defined at points over regions in space. As such, point coordinates now take up the role of independent variables to describe these functions. The previous chapter focused on ‘geometry’, studying how curves and surfaces are situated in space and what features they exhibit. The present chapter assumes this geometry and goes on to explore how the ambient ‘physics’ operates on space, in particular on the curves and surfaces in it. First, ...

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