![]() ![]() If we were to evaluate this line integral without using Green’s theorem, we would need to parameterize each side of the rectangle, break the line integral into four separate line integrals, and use the methods from the section titled Line Integrals to evaluate each integral. Just as with vector line integrals, surface integral \(\displaystyle \iintS \vecs F \cdot \vecs N\, dS\) is easier to compute after surface \(S\) has been parameterized. In short, the plan is Define the concept of flux, physically and mathematically See why an integral is sometimes needed to calculate flux See why in 8. A surface integral over a vector field is also called a flux integral. A conservative formulation of a semi-Lagrangian method was first presented by Leonard et al. \): The line integral over the boundary of the rectangle can be transformed into a double integral over the rectangle. find that flux integrals require a few extra steps in addition to those above to make them easier.
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