MA 242 Test 4 Review Sheet (covers 13.1-13.3, 13.5,10.5 & p.777-778,12.6)

 

Section 13.1 Vector Fields:

á   Sketch the vector field F

á   Be able to find the gradient vector field of f

á   Examples p. 911: 1,3,21,23,25,29,31

 

Section 13.2 Line Integrals:

á   Know how to find the line integral of f along a curve C in R2 (p.913) or R3(p. 918)

á   Be able to find the line integrals with respect to x, y, and z (p. 916)

á   Be able to calculate the mass of a wire using line integrals

á   Understand the definition of path independence (p. 926)

 

á   Find the line integral of a vector field F along C/Find the work done by F moving a particle along a curve

á   Examples p.922: 1,5,11,15,19,33,40,41

 

Section 13.3 The Fundamental Theorem For Line Integrals:

á   Be able to state the result of the Fundamental Theorem for Line Integrals (p.925)

á   Show F(x,y) is or is not conservative (p.928)

á   Given a conservative function F find its potential function f

á   Find the work done by a vector field F moving an object along a curve C

á   Examples p. 932: 3,5,7,13,15,19

 

Section 13.4 GreenÕs Theorem:

á   Know how to use GreenÕs Theorem and what it is (p.934)

á   Green's Theorem Worksheet

 

á   Examples p. 939: 1,2,3,7,9,11,13,15

 

 

Section 13.5 Curl and Divergence:

á   Calculate curl and divergence of F

á   Determine whether F(x,y,z) is conservative or not (p.943)

á   Given a conservative function F find its potential function f

á   Worksheet for 13.3 and Parts of 13.5

 

á   Examples p.947: 1,3,13,15

 

Section 10.5 Parametric Surfaces

á   Find the tangent plane to a parametric surfaces (p.777-778 Examples p.779: 39,41,43)

á   Find a parametric representation of a given surface

á   Examples p.732: 13,14,17,20,21,22,25,26

 

Section 12.6 Surface Area

á   Be able to find the surface area of a parametric surface

á   Examples p. 871:1,3,5,7,11