List of graphics used in Calc III

Chapter 11, Section:

• 1:
  • New England topographical map, sliced
  • Temperature map of U.S.
• 2 and 3:
  • The "wave" for Section 1, in 3 dimensions Winplot version
• 4, 5 and 6: None
• 7:
  • Limits of f(x,y), bad example 1 Winplot version
  • Limits of f(x,y), bad example 2

Chapter 12, Section:

• 1, 2 and 3: None
• 4:
  • Geometric definition of cross product
  • Geometric proof that cross product distributes over vector addition

Chapter 13, Section:

• 1:
  • Approximate partial derivative from a table: why average two difference quotients?
  • Contour diagram: amounts that can be borrowed as a function of interest rates and years of payment Winplot version
• 2: None
• 3:
  • Differential of a function of two variables Winplot version1, 2, 3, 4,
• 4:
  • A surface cut by two vertical planes not parallel to the coordinate planes, and the curves that are cut out Winplot version
  • A function z = f(x,y) not defined on the x- and y-axes, but constant on one line through the origin (so it has a directional derivative on that direction, namely 0) Winplot version
  • Derivation of the formula for a directional derivative
• 5:
  • Two surfaces intersecting in curves
• 6: None
• 7:
  • Why are f_xy(a,b) and f_yx(a,b) usually equal?
• 9:
  • Deriving the Taylor polynomial (in one variable)
  • Taylor polynomials for sin x at x = 0
  • Standard Taylor series at x = 0 (i.e., Maclaurin series)
  • Second-degree Taylor polynomial for e^x+y cos x at (x,y) = (0,0) Winplot version

Chapter 14, Section:

• 1:
  • Two examples of saddle points
  • Derivation of the Second Derivative Test in two variables
• 2: None
• 3:
  • A function on a constrained region in the plane, on which the extrema are sought, Winplot version

Chapter 15, Section:

• 1:
  • Approximating the integral: a function and its corresponding "step" function, Winplot version
  • Graphics for Page 225, Exercise 13:
    • the domains
    • the first graphs
    • the second graphs
• 2:
  • Results of changing the order of integration Winplot version
  • y-coordinate of a center of mass (from class)
• 3 and 5: None
• 6:
  • An increment of volume in spherical coordinates Winplot version