Review for Final Exam
Sections covered  

   * Sections 10.1-10.9, 11.1, 11.3-11.7, 12.1-12.3, 12.4-12.7, 13.1-13.7

To study for the final exam: 

   * Look over the Test 1, 2, 3 Reviews

   * Know the items on this review

   * Go over all your old test questions

   * Try the old test problems that are posted especially the ones you haven't done yet (i.e. problems covering sections 13.5/6/7).

Formulas given on Final exam:  

   * All formulas from previous tests will be given 

   * Formulas given for 13.5/6/7: 

 
                         D 

                         D 

 
     S                                 D 

 
     S                                 D 

 
     S                     D 

 
      S                     D
 
Section 13.3 Line Integrals

1) Memorize that F=<P,Q> is conservative if and only if  

2) Know how to find f(x, y) given F= 

3)
4) Know that if any of the following are true, then all of the following are true and if any of the following are false, then all of the following are false:
       i) F is conservative (i.e. F = gradient of f, or F is a gradient vector field )
      ii)  S F*dr = 0 for any closed path C
           C
      iii)  S F*dr is independent of path
           C
      iv) S F*dr = f(r(b)) - f(r(a))
           C
      v) Py = Qx  for F = < P, Q >

5) Be able to briefly describe how to find a potential function f given a conservative vector field F either by the method I posted or the book's method.

Section 13.4 Green's Theorem
1) Know the definitions for closed curves and simple curves, and be able to identify whether or not a curve is closed or simple.
2) Memoriz and know when you can use Green's theorem:
 S Pdx + Qdy = SS (Qx - Py) dA
C                       D
        C must meet the following criteria:
             i) C must be closed and simple
            ii) C must be counter-clockwise (if not then put a negative sign in front of the integral)
           iii) C must be piecewise smooth

3) Know that D is the area inside of the curve C.

For Section 13.5 you need to know: 

1) Memorize:       

2) Memorize:      

3) Memorize:      
4) Memorize that F is conservative if and only if  

For Section 13.6/13.7 you need to know: 

1) How to use the given surface area formulas, the given surface integral formulas, and the given flux formulas.