Math 236 - Multivariable Calculus
Reading Assignments - January & February 2003
Be sure to check back, because this may change during the semester.
(Last modified:
Wednesday, January 15, 2003,
10:02 AM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Multivariable Calculus by Ostebee/Zorn.
For January 29
Section 1.1 Three-dimensional 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 3-space is a cylinder that is unrestricted in the y-direction.
- Let P be the point in the plane with polar coordinates (1, Pi/2). Give
another pair of polar coordinates for P.
For January 31
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 3
Section 1.2 Curves and parametric equations
Reread the section, but no Reading Questions for today.
For February 5
Section 1.3 Vectors
- To read : All
- Be sure to understand : The section "What is a vector?"
Section 1.4 Vector-valued functions, derivatives, and integrals
- To read : Through Example 3
- Be sure to understand : The section "Derivatives of vector-valued functions"
Reading Questions :
- What are the two quantities associated with a vector?
- Find the unit vector in the direction of the vector v=(12,-5).
- Explain why the velocity of an object moving in 2-space or 3-space is a vector rather than a scalar.
For February 7
Section 1.4 Vector-valued 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 10
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) = (3t2, 7t + t2) 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 12
Work on Group Project 1. No Reading Assignment.
For February 14
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 17
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 19
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 21
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 - x2 a linear function? Why or why not?
- 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 February 24
Section 2.2 Partial derivatives (continued)
Reread the section, but no Reading Questions for today.
For February 26
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)=x2y +3xy-y2
at the point (2,1).
For February 28
Exam 1 today. No reading assignment.
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