1.3 Integral Calculus

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1.3 Integral Calculus
1.3.1 Line, Surface, Volume Integrals
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a) line integral
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Example 1.6
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b) surface integral
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Example 1.7
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volume integral
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Example 1.8
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1.3.3 Fundamental Theorem for Gradients
The line integral does not depend on the path P.
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Example 1.9
along I-II and III
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1.3.4 Fundamental Theorem for Divergences
(also Gausss or Greens theorem)
The surface S encloses the volume V.
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dz
dy
dx
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Example 1.10
Check the divergence theorem for
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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.
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dz
dy
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You must do it in a consistent way!
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Example 1.11
Check Stokes Theorem for