The discussion focuses on the calculation of the differential area element ds for line integrals in various coordinate systems. It establishes that in Cartesian coordinates, ds is represented as dx by dz, while in polar coordinates, it is expressed as rdrdθ. The general procedure for finding ds involves considering the coordinate system used and applying the appropriate Jacobian when necessary, particularly in non-Cartesian systems like spherical coordinates.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are working with vector calculus and need to understand the computation of differential area elements for line integrals.
It s just the area of a rectangular element, dx by dz, in the xz plane. In polar it would have been rdrdθ, etc.Marcin H said:
So what is the general procedure for finding ds? I feel like I struggle determining ds for problems.haruspex said:
It depends on your coordinate system. With general coordinates, ξ, η say, you consider the product dξdη. In general, the area enclosed by the points (ξ,η), (ξ+dξ,η), (ξ+dξ,η+dη), (ξ,η+dη) might have area equal to dξdη. To make the right area you may need to multiply by a Jacobian.Marcin H said: