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Note: Gauss' theorem is also known as the divergence theorem.

- 1 Find the area enlosed by a curve (Green's theorem)
- 2 Line integral over a region (Green's theorem)
- 3 Integrating a vector function given the curl (Stoke's theorem)
- 4 Integrating over a surface (divergence theorem)
- 5 That bathtub question (Stokes' theorem)
- 6 Finding the flux of vector field (divergence theorem)
- 7 Line integral over a 3-dimensional surface (Stokes' theorem)

*1*Find the area enlosed by a curve (Green's theorem)¶

*1.1*Examples¶

- Assignment 2, question 5
- Winter 2010 final, question 5

*2*Line integral over a region (Green's theorem)¶

Use Green's theorem to compute a line integral.

*2.1*General solution¶

The relevant formula is the following:

$$ \oint P\,dx + Q\,dy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\,dA$$

The rest will come later

*2.2*Examples¶

- Assignment 2, questions 6 and 7
- Winter 2006 final, question 5

*3*Integrating a vector function given the curl (Stoke's theorem)¶

*3.1*Examples¶

- Assignment 3, question 1

*4*Integrating over a surface (divergence theorem)¶

*4.1*Examples¶

- Assignment 3, question 2
- Winter 2011 final, question 7

*5*That bathtub question (Stokes' theorem)¶

*5.1*Examples¶

- Assignment 3, question 3

*6*Finding the flux of vector field (divergence theorem)¶

*6.1*Examples¶

- Assignment 3, question 4 (solenoidal in this case)
- Winter 2006 final, question 7
- Winter 2010 final, question 6

*7*Line integral over a 3-dimensional surface (Stokes' theorem)¶

*7.1*Examples¶

- Winter 2006 final, question 8
- Winter 2010 final, question 7 (kind of the opposite of the previous question but I suppose they fit under the same topic)
- Winter 2011 final, question 6 (also requires you to compute the non-line-integral part)