More about Surface Integral
Fluxs
Flux = surface integral of a vector field
Relation to density, volumn and area:
Understand transformation/surface integral#
Break coordinates into one dimensions and think it as a combination of different linear equations.
To compute the area of the parallelogram are determined by the transformation(vectors)#
First, think about how to get the length of vector a;
Question If we describe the distance between (t_A, s_A), and (t_B, s_B) as being dt, how to express a good approximation of vector a?
Then, think about how to compute the length of vector b in the same way.
Finally, combine them, or integrating everything together.
Summary#
Generalizing everything we did in the previous example, the surface area of our parametric surface S is expressed using the integral:
