Calculus III Final Review: Study all old tests and worksheets on my website

 

Section 9.2 Vectors:

á      Given 2 points A and B, find the vector that goes from A to B p. 645

á      Find the magnitude of a vector, find unit vectors

á      Examples p.649: 9, 17, 19, 27, 32

 

Section 9.3 The Dot Product:

á      Know both definitions of the dot product (p. 651 & 653)

á      Be able to determine if 2 vectors are perpendicular or parallel

á      Examples p. 653: 15, 21, 39

 

Section 9.4 The Cross Product:

á      Know the definition and that axb is orthogonal to both a and b.

á      Be able to determine if 2 vectors are parallel

á      Examples p. 661: 7,13,23,27

 

Section 9.5 Equations of Lines and Planes

á      Know both vector and parametric equations of lines

á      Know the scalar equation of the plane

á      Examples p. 671: 3,7,21,23, 25,27

  

Section 10.2 Derivatives and Integrals of Vector Functions

á      Be able to take derivatives and be able to integrate vector functions

á      Know what a tangent vector and a unit tangent vector are

á      Examples p. 706: 9,17,21, 31,33

 

Section 10.4 Motion in Space: Velocity and Acceleration

á      Find the velocity, speed, and acceleration given a position vector

á      Find position, velocity, and speed given acceleration

á      Examples p. 725: 5,9,13,15,21,23

 

Section 11.2 Limits and Continuity:

á   Be able to show a limit does not exist (p.755: 9,13,19)

á   Know the definition of continuity (p.753)

á   Given a function is continuous at (a,b), find its limit there (p.755: 5 & 6)

 

Section 11.3 Partial Derivatives:

á   Know ClairautÕs Theorem (p.763)

á   Be able to take partial derivatives

á   Examples p. 767: 17, 29,31,39,51, 67

 

Section 11.4 Tangent Planes and Linear Approximations:

á   Know how to find the equation of the tangent plane

á   Examples p. 778: 1,4,11,17,19

 

Section 11.5 The Chain Rule

á   Understand the different cases of the chain rule (Case 1, Case 2, the General Case)

á   Examples p. 786: 3,5,13,15

 

Section 11.6 Directional Derivatives and the Gradient Vector

á   Be able to find the derivative of f in the direction of a vector v

á   Know how to maximize the directional derivative (p.795 Theorem 15)

á   Examples p. 799: 11,17,21, 23,31

 

Section 11.7 Maximum and Minimum Values

á   Know the 2nd Derivative Test (p. 803)

á   Be able to identify local maxs, mins, and saddle points

á   Know how to find absolute maxs and mins on a closed bounded set D (p.808)

á   Examples p. 809: 1,27,31 & p.825: 51,53

   

Section 12.3 Double Integrals over General Regions:

á   Be able to set up & integrate double integrals over a region D

á   Be able to find volumes using double integrals

á   Be able to sketch a region D and change the order of integration (p.852: 41,43)

á   Know property 10 on p. 850

á   Examples p. 851: 19,23,29

 

Section 12.4 Double Integrals in Polar Coordinates:

á   Know how to change from rectangular to polar coordinates

á   Examples p. 857: 4,9,15,25

 

Section 12.5 Applications of Double Integrals

á   Given a density function, be able to find the mass and center of mass of a lamina.

á   Examples p. 866: 3,7

 

Section 12.7 Triple Integrals:

á   Be able to set up and evaluate triple integrals, find volume using triple integrals, and find mass of a solid E given a density function.

á   Examples p. 880: 13,17,19

 

Section 9.7 Cylindrical and Spherical Coordinates:

á   You need to know how to convert back and forth between rectangular and cylindrical coordinates and rectangular and spherical coordinates

á   Know the red boxes on pages 682 and 684

 

Section 12.8 Triple Integrals in Cylindrical & Spherical Coordinates

á   You will need to be able to set up and evaluate integrals in both cylindrical and spherical coordinates

á   Examples p. 888: 9,11,19,21,31

 

Section 13.1 Vector Fields:

á   Be able to find the gradient vector field of f

 

 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 calculate the mass of a wire using line integrals

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: 1,13,19,33,41

 

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.929)

á   Given a conservative function F find its potential function f

á   Examples p. 932: 3,5,15,17

 

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   Examples p.947: 1,3, 13, 15

  

Section 13.6 Surface Integrals

á   Compute the surface integral of a parametric surface

á   Take the surface integral of a vector field

á   Examples p.959: 11,13,15,21,23

 

Section 13.7 StokesÕ Theorem

á   Know the result of StokesÕ Theorem (p.961) and be able to use it

          á   Examples p.965: 7,9,13

 

Section 13.8 The Divergence Theorem

          á   Examples p.971: 3,5,7,11,13

 

***NOTE: I will give you StokesÕ Theorem  and the Divergence Theorem but you will need to know how to use them***

 

Other Helpful Information for the Test:

á   Equation and graph of a plane (p.670 box 8)

á   Equation and graph of a paraboloid, cone (p.682)

á   Equation and graph of a sphere (p.640)

á   Equation of a line

á   Equation and graph of a cylinder

á   Sin and Cos at basic angles (See the 2nd reference page at the very front of your book)

á   U-substitution

á   Integration by Parts