HTSEFP: Green, Gauss and Stokes theorems

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

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

1.1Examples¶

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

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

Use Green's theorem to compute a line integral.

2.1General 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

2.2Examples¶

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

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

3.1Examples¶

• Assignment 3, question 1

4Integrating over a surface (divergence theorem)¶

4.1Examples¶

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

5That bathtub question (Stokes' theorem)¶

5.1Examples¶

• Assignment 3, question 3

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

6.1Examples¶

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

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

7.1Examples¶

• 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)