### Math 236 - Multivariable Calculus Reading Assignments - January & February 2002

Be sure to check back, because this may change during the semester.

All numbers indicate sections from Multivariable Calculus by Ostebee/Zorn.

### For January 30

Section 1.1 Three-dimensional space
• Be sure to understand : The section "Equations and their graphs"

Appendix A Polar coordinates and polar curves

• Be sure to understand : The section "Trading polar and rectangular coordinates"

1. Give an example of an equation whose graph in 3-space is a cylinder that is unrestricted in the y-direction.
2. 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
• Be sure to understand : Examples 1, 4, and 7. The section "Tricks of the trade"

1. Is every parametric curve the graph of a function y=f(x)? Why or why not?
2. Can every graph y=f(x) be expressed in parametric form? Why or why not?
3. Give a parametrization of the line connecting the points P=(-1,2) and Q=(3,0).

### For February 4

Section 1.3 Vectors
• Be sure to understand : The section "What is a vector?"

1. What are the two quantities associated with a vector?
2. Find the unit vector in the direction of the vector v=(12,-5).

### For February 6

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"

1. Consider the line in 3-space that contains the point (1,2,3) and has direction (2,1,3). Give a vector valued equation for this line.
2. Explain why the velocity of an object moving in 2-space or 3-space is a vector rather than a scalar.

### For February 8

Section 1.4 Vector-valued functions, derivatives, and integrals
• To read : Finish the section
• Be sure to understand : The section "Interpreting the difference quotient"

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
• 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.

1. What is the velocity of the particle at time t=5?
2. What is its speed at time t=5?
3. 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
• Be sure to understand : The sections "Geometry of the dot product" and "Projecting one vector onto another"

1. If u and v are unit vectors, what geometric quantity does the dot product of u and v measure?
2. 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
• Be sure to understand : The section "Planes"

1. What information about a line L do you need to determine an equation for the line?
2. 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
• Be sure to understand : The definition of the cross product,

1. How is u x v related to u and v geometrically?
2. Why are we studying the cross product now?

### For February 22

Section 2.1 Functions of several variables Section 2.2 Partial Derivatives
• 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

1. Is N(x,y) = 3x + 5y - x2 a linear function? Why or why not?
2. 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 25

Section 2.2 Partial derivatives (continued)
• Be sure to understand : Examples 4 & 5, the statement of Theorem 1

Find all stationary points of f(x,y)=x2 +2xy+y2

### For February 27

Section 2.3 Partial derivatives and linear approximations