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# PH 333 Integral Calculus

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## Richard Datwyler

on 21 September 2017

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#### Transcript of PH 333 Integral Calculus

Types of integrals
Line
Surface
Volume
open
closed
dl depends on the path you take.
closed paths start and stop at the same location
da depend on the surface

closed surfaces have distinct outsides and insides, think balloon or box
Can 'act' on a vector or scalar
Line integral
Show that the gradient theorem is independent of path by taking the function F = 2y + 3xy - 7xz on the two paths shown to the location (1,1,2).
2
-9
-9
-9
Surface integrals
Prove Stokes theorem by computing the surface and line integral of the vector
on the surface shown here
2
1
-8
Volume Integrals
Prove the divergence theorem by taking the volume integral of the divergence of vector
over the rectangular prism with internal vector (1,2,3)
3
2
1
-114
Integral Calculus
Integration by Parts
moves the derivative around, try it here on a sphere of radius R.
Full transcript