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 :

  1. How is u x v related to u and v geometrically?
  2. 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.

  1. Find fx(x,y) and fy(x,y).
  2. 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).

  1. What type of quantity is the gradient of f at (1,2)?
  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 :

  1. What information does the directional derivative give you?
  2. 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:

  1. If f(x,y)=x3y2+2xy, what is fxy?
  2. 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.


Math 236 Home | T. Ratliff's Home
Maintained by Tommy Ratliff, tratliff@wheatonma.edu
Last modified: Monday, August 20, 2001, 7:45 PM