Review Sheet for Test 3                                                       Spring 2007

(Sections 16.7-17.6)

 

16.7        Know how to do triple integrations.

Know how to find the bounding surfaces.

Know how to find the region D (that is, the projection of the solid).

Know how to find the volume, the mass, and the center of mass of a solid.

16.8        Know how to use spherical and cylindrical coordinates for triple integration.

17.1        Know the definition of a conservative vector field.

You will not be asked to sketch vector fields.

17.2        Be able to compute line integrals for functions and for vector fields.

Know the meaning of line integrals (work, mass and center of mass of a wire).

Know how to parameterize a circle.

Know how to parameterize a line segment between two given points.

17.3        KNOW and UNDERSTAND the statement of the Fundamental Theorem for Line Integrals (that is, Theorem 2 on page 1110).

KNOW and UNDERSTAND its proof.

Know that the line integral of a conservative vector field over a closed curve is 0 (why?)

Know that the line integral of a conservative vector field is path independent (why?)

Know how to find a potential function f.

17.4        Know GreenŐs Theorem.

Be able to do all the HW assignments.

17.5        Know the definition of div and curl.

            Know that a vector field F defined on R^3 is conservative if curl F=0 (why?)

Know how to find a potential function if F is conservative.

17.6        Know how to find parametric equations of a sphere, a cylinder (along the x, y, or z-axis),

            a surface given by z=g(x,y), or y=g(x,z), or x=g(y,z).

Know how to find the equation of a tangent plane for a parametric surface.

            Know how to compute the surface area of a surface

 

 

Make statements on your test. (For instance: Write equal signs whenever you think two expressions are equal.) Use a pencil and write legibly.