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1.3 Integral Calculus 1.3.1 Line, Surface, Volume Integrals
For a given boundary line there many different surfaces, on which the surface integral depends. It is independent only if If the surface is closed: b) surface integral:
2 2 2 Example 1.7
1.3.3 Fundamental Theorem for Gradients The line integral does not depend on the path P.
Example 1.9 along I-II and III
1.3.4 Fundamental Theorem for Divergences (also Gauss’s or Green’s theorem) The surface S encloses the volume V.
dz dy dx
Example 1.10 Check the divergence theorem for
1.3.5 Fundamental Theorem for Curls (also Stokes’ theorem) The path P is the boundary of the surface S. The integral does not depend on S.
Example 1.11 Check Stokes’ Theorem for