MA 242 Honors Test 4 Review Sheet (covers 13.1-13.4, 13.5,10.5 & p.777-778,12.6)

Section 13.1 Vector Fields:

· Sketch the vector field F

· Be able to find the gradient vector field of f

· Examples p. 910: 1,3,21,25,29,31

Section 13.2 Line Integrals:

· Know how to find the line integral of f along a curve C in R² (p.913) or R³(p. 917)

· Be able to find the line integrals with respect to x, y, and z (p. 915)

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

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

· Examples p.921: 1,11,17,27,35, 39

Section 13.3 The Fundamental Theorem For Line Integrals:

· Be able to state the result of the Fundamental Theorem for Line Integrals (p.924)

· Be able to prove the Fundamental Theorem for Line Integrals (p.925, We did this proof in class)

· Understand the definition of path independence (p. 925)

· Be able to prove Theorem 5 (p. 927, We did this proof in class)

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

· Given a conservative function F find its potential function f

· Examples p. 931: 3,5,15,17,23, 27,29,33

Section 13.4 Green’s Theorem:

· Know how to use Green’s Theorem and what it is (p.933)

· Examples p. 939: 1,3,7,9,11,13,15,17

Section 13.5 Curl and Divergence:

· Calculate curl and divergence of F

· Determine whether F(x,y,z) is conservative or not (p.942)

· Given a conservative function F find its potential function f

· Be able to prove Theorem 11 (p. 943, we did this in class)

· Worksheet for 13.3 and Parts of 13.5

· Examples p.947: 1,3, 13, 15,17,36

Section 10.5 Parametric Surfaces

· Find the tangent plane to a parametric surfaces (p.777-778 Examples p.779: 33,35,37)

· Find a parametric representation of a given surface

· Examples p.733: 11,12,14,15,19,23,24,29

Section 12.6 Surface Area

· Be able to find the surface area of a parametric service

· Examples p. 871:1,3,7,11