Calculus Volume 3 · free preview
Stokes' Theorem
Stokes' theorem converts the circulation around a space curve to the curl's flux through any spanning surface, the Green's theorem's space generalization, with the boundary's orientation the compatible right-handed one.
1. The theorem
The theorem
2. Verification and examples
Verification and examples
3. Relation to Green and the conservatism
Relation to Green and the conservatism
4. The generalized Stokes' pattern
The generalized Stokes' pattern
5. Stokes statement
Stokes' theorem equates the circulation around C to which surface integral?
6. Surface independence
Stokes' theorem implies the curl's flux through S depends only on what?
7. Orientation compatibility
In Stokes' theorem, the surface's normal and the boundary's orientation are related how?
8. Green's theorem relation
Green's theorem is Stokes' theorem in which special case?
9. Tactical use
When is Stokes' theorem most profitably applied?
10. Curl flux boundary
The curl's flux through S equals the boundary's which integral? Answer with one word.
11. Two dimensional curl z
For a plane field, the curl is in the z direction with magnitude Q_x minus P_y. As a single letter, which axis? Answer with one lowercase letter.
12. Closed surface curl flux
The curl's flux through a closed surface is zero. As a number, what is it? Answer with a number.
13. Ampere-Maxwell connection
In electromagnetism, Stokes' theorem converts Ampere's law, the magnetic circulation around a loop, to which integral?
14. Right hand thumb
In the right-hand rule, the thumb points along which vector? Answer like the normal.
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