Math 236 - Multivariable Calculus
Reading Assignments - October 2001
Be sure to check back, because this may change during the semester.
(Last modified:
Monday, August 20, 2001,
7:45 PM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Multivariable Calculus by Ostebee/Zorn.
For October 1
Section 1.8 The cross product
Section 2.1 Functions of several variables
- To read : All
- Be sure to understand : The definition of the cross product,
the section "Level curves and contour maps" in Section 2.1
Email Subject Line : Math 236 10/1 Your Name
Reading Questions :
- How is u x v related to u and v geometrically?
- Is N(x,y) = 3x + 5y - x2 a linear function? Why or why not?
For October 3 & 5
No reading assignments for these days.
For October 10
Section 2.2 Partial Derivatives
- To read : All
- Be sure to understand : Example 2, the formal definition of partial derivatives
Reading Questions : Since this is the first day back from break,
you don't have to send these in, but you should think about them.
Let f(x,y)=x2y + 3xy - y.
- Find fx(x,y) and fy(x,y).
- Is f increasing or decreasing in the x direction at the point (2,1)? Why?
For October 15
Section 2.2 Partial derivatives (continued)
- To read : Reread the section
- Be sure to understand : Examples 4 & 5, the statement of Theorem 1
Email Subject Line : Math 236 10/15 Your Name
Reading Question :
Find all stationary points of f(x,y)=x2 +2xy+y2
For October 17
Section 2.3 Partial derivatives and linear approximations
- To read : All
- Be sure to understand : The section "Partial derivatives, the cross product,
and the tangent plane" and the defintion of linear approximation
Email Subject Line : Math 236 10/17 Your Name
Reading Question :
Find the linear approximation to f(x,y)=x2y +3xy-y2
at the point (2,1).
For October 19
Takehome exam due today. No reading assignment.
For October 22
Section 2.4 The gradient and directional derivatives
- To read : All
- Be sure to understand : The definition of the gradient
Email Subject Line : Math 236 10/22 Your Name
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 October 24
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"
Email Subject Line : Math 236 10/24 Your Name
Reading Questions :
- What information does the directional derivative give you?
- For a function f(x,y), how many components does the gradient
vector contain?
For October 26
Section 2.5 Local Linearity: theory of the derivative
- To read : All
- Be sure to understand : Example 1, the definition of the total derivative
Email Subject Line : Math 236 10/26 Your Name
Reading Question:
What is the point of Example 1?
For October 29
Section 2.6 Higher Order Derivatives and Quadratic Approximations
- To read : All
- Be sure to understand : The statement of Theorem 2, and the section
"Taylor polynomials in several variables"
Email Subject Line : Math 236 10/29 Your Name
Reading Questions:
- If f(x,y)=x3y2+2xy, what is fxy?
- Is there a function f(x,y) where fxy=2xy+y and
fyx=x2y+x? Explain.
For October 31
Work on Project 2 - No reading assignment.
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