Math 236  Multivariable Calculus
Reading Assignments  January & February 2002
Be sure to check back, because this may change during the semester.
(Last modified:
Sunday, January 20, 2002,
11:32 AM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Multivariable Calculus by Ostebee/Zorn.
For January 30
Section 1.1 Threedimensional space
 To read : All
 Be sure to understand : The section "Equations and their graphs"
Appendix A Polar coordinates and polar curves
 To read : All
 Be sure to understand : The section "Trading polar and rectangular coordinates"
Reading Questions :
 Give an example of an equation whose graph in 3space is a cylinder that is unrestricted in the ydirection.
 Let P be the point in the plane with polar coordinates (1, Pi/2). Give
another pair of polar coordinates for P.
For February 1
Section 1.2 Curves and parametric equations
 To read : All
 Be sure to understand : Examples 1, 4, and 7. The section "Tricks of the trade"
Reading Questions :
 Is every parametric curve the graph of a function y=f(x)? Why or why not?
 Can every graph y=f(x) be expressed in parametric form? Why or why not?
 Give a parametrization of the line connecting the points P=(1,2) and Q=(3,0).
For February 4
Section 1.3 Vectors
 To read : All
 Be sure to understand : The section "What is a vector?"
Reading Questions :
 What are the two quantities associated with a vector?
 Find the unit vector in the direction of the vector v=(12,5).
For February 6
Section 1.4 Vectorvalued functions, derivatives, and integrals
 To read : Through Example 3
 Be sure to understand : The section "Derivatives of vectorvalued functions"
Reading Questions :
 Consider the line in 3space that contains the point (1,2,3) and has direction (2,1,3). Give a vector valued equation for this line.
 Explain why the velocity of an object moving in 2space or 3space is a vector rather than a scalar.
For February 8
Section 1.4 Vectorvalued functions, derivatives, and integrals
 To read : Finish the section
 Be sure to understand : The section "Interpreting the difference quotient"
Reading Question :
Use vector derivatives to find a vector equation for the line tangent to the unit circle
at (1/2, sqrt(3)/2).
For February 11
Section 1.5 Derivatives, antiderivatives, and motion
 To read : All
 Be sure to understand : The section "Speed and arclength" and Example 9
Reading Questions Let p(t) = (3t^{2}, 7t + t^{2}) give the position of a particle at time t.
 What is the velocity of the particle at time t=5?
 What is its speed at time t=5?
 Approximately how far has it traveled from time t=1 to t=5?
For February 13
Work on Group Project 1. No Reading Assignment.
For February 15
Section 1.6 The dot product
 To read : All
 Be sure to understand : The sections "Geometry of the dot product" and "Projecting one vector onto another"
Reading Questions :
 If u and v are unit vectors, what geometric quantity does
the dot product of u and v measure?
 Let v=(3,4) and w=(5,2). Find the component of v in the
w direction.
For February 18
Section 1.7 Lines and planes in three dimensions
 To read : All
 Be sure to understand : The section "Planes"
Reading Questions :
 What information about a line L do you need to determine an equation for the line?
 What information about a plane P do you need to determine an equation for the plane?
For February 20
Section 1.8 The cross product
 To read : All
 Be sure to understand : The definition of the cross product,
Reading Questions :
 How is u x v related to u and v geometrically?
 Why are we studying the cross product now?
For February 22
Section 2.1 Functions of several variables
Section 2.2 Partial Derivatives
 To read : All
 Be sure to understand : The section "Level curves and contour maps"
in Section 2.1, Example 2 in Setion 2.2, and the formal definition of partial derivatives
Reading Questions :
 Is N(x,y) = 3x + 5y  x^{2} a linear function? Why or why not?
 Let f(x,y)=x^{2}y + 3xy  y.
Find f_{x}(x,y) and f_{y}(x,y).
Is f increasing or decreasing in the x direction at the point (2,1)? Why?
For February 25
Section 2.2 Partial derivatives (continued)
 To read : Reread the section
 Be sure to understand : Examples 4 & 5, the statement of Theorem 1
Reading Question :
Find all stationary points of f(x,y)=x^{2} +2xy+y^{2}
For February 27
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
Reading Question :
Find the linear approximation to f(x,y)=x^{2}y +3xyy^{2}
at the point (2,1).
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