Stokes’ theorem says we can calculate the flux of curl F across surface S by knowing information only about the values of F along the boundary of S. Conversely, we can calculate the line integral of vector field F along the boundary of surface S by translating to a double integral of the curl of F over S.
Let S be an oriented smooth surface with unit normal vector N. Furthermore, suppose the boundary of S is a simple closed curve C. The orientation of S induces the positive orientation of C if, as you walk in the positive direction around C with your head pointing in the direction of N, the surface is always on your left. With this definition in place, we can state Stokes’ theorem.
source: 6.7 Stokes’ Theorem - Calculus Volume 3 | OpenStax
When it comes to teaching Stokes' Theorem and its applications in CEng engineering, there are several methodologies and tools that can be utilized to make the learning experience more engaging and effective. Here are a few examples:
References:
- OpenStax Calculus Volume 3, Chapter 6.7, "Stokes' Theorem"
- Wolfram Demonstrations Project: "Stokes' Theorem"
- "Stokes' Theorem Explained" by Math Fortress on YouTube.
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