MAC 2313 - Section 03 - Fall 2003
Related Pages: Course Home Page | Syllabus | Homework
Calculators will be allowed for the test.
Chapter 12 - Functions of Several Variables (skip 12.6)
Functions of Several (2 or More) Variables
be able to investigate, interpret, plot and visualize
functions of several variables (including linear functions)
cross-sections
contours: level curves, level surfaces
tables
graphs
formulas
surfaces on page 593 and planes
distance between 2 points
Linear Functions
planes
recognize and determine equation of a plane from
contour/cross-section diagrams, tables, graphs, formulas
See also Chapter 12 Summary on page 600
Review Homework for Chapter 12, pg 600: #2 ,3, 5,
7, 9, 11, 13, 15, 17, 21
Chapter 13 - Vectors (all sections)
Vectors
vector properties: addition, subtraction, scalar multiplcation, zero vector
vector components, resolving a vector into components
vector between 2 points (displacement vectors)
magnutide
unit vector
dot product: geometric and algebraic definitions, interpretation and
properties
cross product: geometric and algebraic definitions, interpretation and
properties
normal vector
applications: vectors in n dimensions, dot product,
angle between 2 vectors, perpendicularity, normal vectors, work,
vector problems dealing with velocity and direction of heading, equation
of a plane, area of a rectangle or triangle, volume of a parallelepiped
See also Chapter 13 Summary on page 635
Review Homework for Chapter 13, pg 635: #1-17 odds, 14, 23, 24, 27, 29, 33
Chapter 14 - Differentiating Functions of Several Variables (all sections)
Partial Derivatives
definition
interpretation
compute numerically and algebraically
second order and higher partial derivatives (including interpretations)
chain rule
differentiability of a function
Applications
linear approximation to a curve (local linearity/tangent plane approximation)
differential
directional derivative: definition, interpretation, compute numerically
and algebraically
gradient vector: definition, interpretation (geometric properties)
tangent plane
Taylor approximations
See also Chapter 14 Summary on page 694
Review Homework for Chapter 14, pg 695: #1, 3, 5, 9, 11, 13, 15, 17, 19,
21, 23, 27, 31, 41, 45, 51
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