SECTION

CONCEPTS

METHODS

12.1
Functions of Two Variables

• right-handed axis system

• locating points
• distance between points

12.2
Graphs of Functions of Two Variables

• independent and dependent variables
• domain
• cylinders

• drawing cross sections
• looking for a missing variable

12.3
Contour Diagrams

• level curves f(x,y)=c

• drawing a collection of level curves
• interpreting a contour plot

12.4
Linear Functions

• The graph is a plane
• z = ax+by+c  pattern
• slope in x-direction, slope in y-direction

• finding an equation for a plane through given points
• recognizing the contour plot of a plane

12.5
Functions of Three Variables

• level surfaces

• finding equations of level surfaces
• converting from z=f(x,y) to g(x,y,z)=c, and vice-versa

12.6
Limits and Continuity

• approaching a limit from different directions
• discontinuities

• calculating limits from different directions
• recognizing continuous functions

13.1
Displacement Vectors

• direction and magnitude

• calculating magnitude
• adding and subtracting vectors
• finding scalar multiples of v; these are parallel to v
• writing vectors in i, j, k components

13.2
Vectors in General

• velocity
• basic properties of vector arithmetic

• combining vectors algebraically
• combining vectors geometrically
• resolving a vector into i, j, k components

13.3
Dot Product

• algebraic definition
• geometric definition
• orthogonal vectors
• normal vector to a plane

• calculating by algebraic definition
• finding the angle between two vectors
• checking orthogonality, finding perpendicular vectors
• using dot product to write an equation for a plane

13.4
Cross Product

• right-handed triple of vectors
• anticommutative
• area of a parallelogram

• computing the cross product
• computing area
• finding normal vectors to a plane