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Reading Assignments - Math 236 Multivariable Calculus - Spring 2011

Be sure to check back, because this may change during the semester.
(Last modified: Sunday, July 31, 2011, 8:58 PM )

I'll use Maple syntax for mathematical notation on this page. All numbers indicate sections from Multivariable Calculus, Early Transcendental Functions 3e by Smith and Minton.

For Friday January 28

Section 10.1 Vectors in the Plane
Section 10.2 Vectors in Space
Section 10.3 The Dot Product

To read: All

Reading Questions:
Let a, b, and c be vectors, and let a.b denote the dot product.

  1. Is (a.b).c the same as a.(b.c)?
  2. In what direction does projba point?
  3. When is compba equal to compab?

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For Monday January 31

Section 10.4 The Cross Product

To read: All

Reading Questions:

  1. How is axb related to a and b geometrically?
  2. Why don't we define axb for vectors in the plane?

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For Wednesday February 2

Section 10.5 Lines and Planes in Space

To read: All

Reading Questions:

  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?

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For Friday February 4

Section 11.1 Vector-Valued Functions

To read: All

Reading Questions:

  1. Consider the graph of the vector-valued function r(t)=cos(t)i - sin(t)j. Is this the graph of a function y=f(x)? Explain.
  2. Describe the curve traced out by r(t) = < t, cos(t), sin(t)>, t≥ 0.

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For Monday February 7

Section 11.2 The Calculus of Vector-Valued Functions

To read: All

Reading Questions:

  1. If r(t) is a vector-valued function, what geometric information does r'(t) give you?
  2. If the graphs of r(t) and s(t) are the same, will r'(0) always be the same as s'(0)? Explain.

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For Wednesday February 9

Section 11.3 Motion in Space

To read: All. Be sure to understand Examples 3.4 and 3.5.

Reading Questions:

  1. What quantity does the magnitude of the velocity vector give?
  2. In Example 3.4, how would a headwind (i.e. a wind blowing directly opposite the direction of travel) affect the calculations?

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For Friday February 11

Section 11.4 Curvature

To read: All

Reading Questions:

  1. Explain the idea of curvature in your own words.
  2. If the helix in Example 4.5 were changed to r(t)=< 2sin(t), 2cos(t), 4t2 > , will the curvature still be constant? Don't actually do the calculation, but give an intuitive justification.

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For Monday February 14

Work on Project 1 today. No Reading Assignment.

For Wednesday February 16

Section 11.5 Tangent and Normal Vectors

To read: Through the section Tangential and Normal Components of Acceleration.

Reading Questions:

  1. Suppose you are skiing down a hill that curves left. Describe the directions of the unit tangent, principle unit normal, and binormal vectors.
  2. Why do you want the normal component of acceleration to be small when steering a car through a curve?

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For Friday February 18

Finish reading the section, but no Reading Questions for today.

For Monday February 21

Section 10.6 Surfaces in Space

To read: All

Reading Questions:
Consider the surface y=x2 + z2

  1. What does the trace in the xy-plane look like?
  2. What do the traces in the planes y=k look like?

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For Wednesday February 23

Section 12.1 Functions of Several Variables

To read: All

Reading Questions:

  1. Is a hyperboloid of one sheet the graph of a function of two variables? Explain.
  2. How can you identify the local extrema of f(x,y) from its contour plot?

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For Friday February 25

Section 12.2 Limits and Continuity

To read: All

Reading Questions:

  1. What is the point of Example 2.5?
  2. Why do you think we are studying limits now?

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For Monday February 28

Inclass part of Exam 1. No Reading Assignment.

For Wednesday March 2

Section 12.3 Partial Derivatives

To read: All

Reading Questions:

  1. For f(x,y), what information does fx(1,0) give?
  2. How many second-order partial derivatives does g(x,y,z) have?

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For Friday March 4

Reread Section 12.3, but no Reading Questions for today.

For Monday March 7

Section 12.4 Tangent Planes and Linear Approximations

To read: All

Reading Questions:

  1. If f(x,y) is a well-behaved function and has a local maximum at (a,b), what can you say about the linear approximation to f(x,y) at (a,b)?
  2. Let L(x,y) be the linear approximation of f(x,y) at (a,b). What graphical properties of the surface z=f(x,y) would make L(x,y) particularly accurate? particularly inaccurate?

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For Wednesday February 9

Section 12.5 The Chain Rule

To read: All

Reading Question:

Suppose that w=f(x,y,z) and that x,y,z are all function of r,s,t. How many partial derivatives do you need to calculate in order to determine dw/dt?

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For Friday March 11

No Reading Assignment for today.

For March 14 - 18

Spring Break!

For Monday March 21

Section 12.6 The Gradient and Directional Derivatives

To read: All

Reading Questions:

  1. Explain the idea of a directional derivative your own words.
  2. What type of quantity is the gradient of a function f(x,y)?
  3. What information does the gradient give you about f(x,y)?

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For Wednesday March 23

Section 12.7 Extrema of Functions of Several Variables

To read: All

Reading Questions:

  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. Suppose that f is a well-behaved function where fx(3,4)=0, fy(3,4)=0, fxx(3,4)=2, fyy(3,4)=-3, and fxy(3,4)=-2. Will (3,4) be a local max, min, or neither of f? Why?
  3. Explain the idea behind the method of steepest ascent in your own words.

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For Friday March 25

Reread Section 12.7, but no Reading Questions for today.

For Monday March 28

Work on Project 2 today. No Reading Assignment.

For Wednesday March 30

Section 13.1 Double Integrals

To read: All

Reading Questions:

  1. If f(x,y) is a function of two variables, what does ∫∫R f(x,y) dA measure?
  2. Explain Fubini's Theorem in your own words. What is its importance?

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For Friday April 1

Reread Section 13.1, paying especial attention to Example 1.7, but no Reading Questions for today.

For Monday April 4

Section 9.4 Polar Coordinates
Section 9.5 Calculus in Polar Coordinates

To read: All, but you can de-emphasize the beginning of Section 9.5 on differentiation in polar coordinates.

Reading Questions:

  1. What do the coordinates (r,theta) in polar coordinates measure?
  2. Why does finding area by integration in polar coordinates differ from finding area by integration in rectangular coordinates?

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For Wednesday April 6

Section 13.3 Double Integrals in Polar Coordinates

To read: All

Reading Questions:

  1. Why would you want to convert a double integral from rectangular to polar coordinates?
  2. What is the shape of a polar rectangle?

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For Friday April 8

Reread Section 13.3, but no Reading Questions for today.

For Monday April 11

Section 13.4 Surface Area

To read: All

Reading Questions:

  1. Give a real-world example where you would want to compute surface area.
  2. After partitioning the region R, what object is used to approximate the surface area over each subregion Ri?

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For Wednesday April 13

Section 14.1 Vector Fields

To read: All

Reading Questions:

  1. Explain why Graph B in Example 1.3 is not the actual graph of a vector field but is just a representation of the graph of a vector field.
  2. If a particle is dropped onto Figure 14.7a at the point (-1,1), describe the path the particle will follow.

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For Friday April 15

Section 14.2 Line Integrals

To read: All

Reading Question:

Give two different uses for the line integral.

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For Monday April 18

Inclass part of Exam 2. No Reading Assignment

For Wednesday April 20

Reread Section 14.2, but no Reading Questions for today.

For Friday April 22

Section 14.3 Independence of Path and Conservative Vector Fields

To read: All

Reading Questions:

  1. Why are conservative vector fields your friend when evaluating line integrals?
  2. Why is Theorem 3.2 call the Fundamental Theorem for line integrals?

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For Monday April 25

Reread Section 14.3, but no Reading Questions for today.

For Wednesday April 27

Section 14.4 Green's Theorem

To read: All

Reading Questions:

  1. What surprises you about Green's Theorem?
  2. Give an example of a region R in the plane where Green's Theorem does not hold.

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For Friday April 29

Reread Section 14.4, but no Reading Questions for today.

For Monday May 2 and Wednesday May 4

No Reading Assignment.

For Friday May 6

The BIG Picture for the course

No reading for today
Last Modified: Sunday, July 31, 2011, 8:58 PM
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