Math 236  Multivariable Calculus
Reading Assignments  March 2002
Be sure to check back, because this may change during the semester.
(Last modified:
Sunday, January 20, 2002,
11:49 AM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Multivariable Calculus by Ostebee/Zorn.
For March 1
Exam 1 today. No reading assignment.
For March 4
Section 2.4 The gradient and directional derivatives
 To read : All
 Be sure to understand : The definition of the gradient
Reading Questions : Suppose (1,2) is a point in the domain of the fuction f(x,y).
 What type of quantity is the gradient of f at (1,2)?
 How is the gradient at (1,2) related to the level curve through (1,2)?
For March 6
Section 2.4 The gradient and directional derivatives (continued)
 To read : Reread the section
 Be sure to understand : The section "Gradient vectors and linear approximation"
Reading Questions :
 What information does the directional derivative give you?
 For a function f(x,y,z), how many components does the gradient
vector contain?
For March 8
Section 2.5 Local Linearity: theory of the derivative
 To read : All
 Be sure to understand : Example 1, the definition of the total derivative
Reading Question:
What is the point of Example 1?
For March 11, 13, & 15
Spring Break, so obviously no reading assignment.
For March 18
Section 2.7 Maxima, Minima, and Quadratic Approximation
 To read : Through Example 5
 Be sure to understand : Examples 2 and 3
Reading Questions:
 If the partials f_{x} and f_{y} exist everywhere,
at what points (x_{0}, y_{0}) can f have a local max or
a local min?
 Why does the term "saddle point" make sense?
For March 20 & 22
Work on Project 2  No reading assignment.
For March 25
Section 2.8 The Chain Rule
 To read : All
 Be sure to understand : The definition of the derivative matrix, the statement of the Chain Rule (Theorem 4), and Example 5.
Reading Questions:
 If f:R^{5} > R^{3}, how many rows does the derivative matrix of
f contain? How many columns?
 If f:R^{3} > R^{4} and g:R^{4} > R^{5}, what will the dimensions of the derivative matrix of g o f be?
For March 27
Section 3.1 Multiple Integrals and Approximating Sums
 To read : All
 Be sure to understand : The section Approximating Sums on page 173 and the definition of the double integral as a limit on page 175
Reading Question:
 If f(x,y) is a function of two variables, what does _{R} f(x,y) dA measure?
 For any region R in the plane, what does
_{R} 1 dA measure?
For March 29
Section 3.2 Calculating Integrals by Iteration
 To read : All
 Be sure to understand : The section "Iteration: why it works"
Reading Question:
What is the advantage of calculating double integrals by iteration?
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