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1.3 Integral Calculus

1.3 Integral Calculus. 1.3.1 Line, Surface, Volume Integrals. a) line integral:. Example 1.6. 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.

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1.3 Integral Calculus

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  1. 1.3 Integral Calculus 1.3.1 Line, Surface, Volume Integrals

  2. a) line integral:

  3. Example 1.6

  4. 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:

  5. 2 2 2 Example 1.7

  6. volume integral:

  7. Example 1.8

  8. 1.3.3 Fundamental Theorem for Gradients The line integral does not depend on the path P.

  9. Example 1.9 along I-II and III

  10. 1.3.4 Fundamental Theorem for Divergences (also Gauss’s or Green’s theorem) The surface S encloses the volume V.

  11. dz dy dx

  12. Example 1.10 Check the divergence theorem for

  13. 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.

  14. dz dy

  15. You must do it in a consistent way!

  16. Example 1.11 Check Stokes’ Theorem for

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