### Math 236 - Multivariable Calculus Reading Assignments - March 2002

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

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

### For March 1

Exam 1 today. No reading assignment.

### For March 4

Section 2.4 The gradient and directional derivatives
• Be sure to understand : The definition of the gradient

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 March 6

Section 2.4 The gradient and directional derivatives (continued)
• Be sure to understand : The section "Gradient vectors and linear approximation"

1. What information does the directional derivative give you?
2. For a function f(x,y,z), how many components does the gradient vector contain?

### For March 8

Section 2.5 Local Linearity: theory of the derivative
• Be sure to understand : Example 1, the definition of the total derivative

What is the point of Example 1?

### For March 11, 13, & 15

Spring Break, so obviously no reading assignment.

### For March 18

Section 2.7 Maxima, Minima, and Quadratic Approximation
• To read : Through Example 5
• Be sure to understand : Examples 2 and 3

1. If the partials fx and fy exist everywhere, at what points (x0, y0) can f have a local max or a local min?
2. Why does the term "saddle point" make sense?

### For March 20 & 22

Work on Project 2 - No reading assignment.

### For March 25

Section 2.8 The Chain Rule
• Be sure to understand : The definition of the derivative matrix, the statement of the Chain Rule (Theorem 4), and Example 5.

1. If f:R5 -> R3, how many rows does the derivative matrix of f contain? How many columns?
2. If f:R3 -> R4 and g:R4 -> R5, what will the dimensions of the derivative matrix of g o f be?

### For March 27

Section 3.1 Multiple Integrals and Approximating Sums
• Be sure to understand : The section Approximating Sums on page 173 and the definition of the double integral as a limit on page 175

1. If f(x,y) is a function of two variables, what does R f(x,y) dA measure?
2. For any region R in the plane, what does R 1 dA measure?

### For March 29

Section 3.2 Calculating Integrals by Iteration