For September 5

Section 1.1 Three-dimensional space

• To read: All
• Major ideas
  • Cartesian coordinates in three dimensions
  • The equations of planes, spheres, and cylinders in three dimensions

Section 1.2 Functions of several variables

• To read: All
• Major ideas
  • Graphs of functions of two variables
  • Level curves and contour maps of f(x,y)
  • Definition of a linear function in two variables

Email Subject Line: Math 236 9/5 Your Name

For September 8

• To read: Through Example 3
• Major ideas:
  • The graph of a function of two variables can be approximated by a tangent plane
  • The definition of the partial derivatives of f(x,y)
  • Approximating f_x and f_y from tables and contour plots

Email Subject Line: Math 236 9/8 Your Name

For September 10

• To read: The rest of the section
• Major ideas:
  • Using partial derivatives to build a linear approximation of f(x,y)

Email Subject Line: Math 236 9/10 Your Name

For September 12

Section 1.4 Optimization and partial derivatives: a first look

• To read: All
• Major ideas:
  • The definition of stationary points for a function of two variables
  • Identifying stationary points as local maxima, minima or saddle points from a contour plot

Email Subject Line: Math 236 9/12 Your Name

For September 15

For September 17

For September 19

• To read: All
• Major ideas
  • The polar coordinate system for the plane
  • Polar plots
  • Converting polar coordinates to/from rectangular coordinates

Email Subject Line: Math 236 9/19 Your Name

For September 22

• To read: All
• Major ideas
  • Motivation for parametric equations
  • Some sample parametrizations
  • The same curve may have many different parametrizations

Email Subject Line: Math 236 9/22 Your Name

Reading Questions:

1. Follow Example 3 to parametrize the line segment from P=(1,2) to Q=(5,-4).
2. Give a parametrization of the circle of radius 2 centered at (3,1).

For September 24

• To read: All
• Major ideas
  • Introduction to vectors
  • Algebra with vectors
  • Vector-valued functions and their derivatives

Section 2.3 The dot product

• To read: All
• Major ideas
  • The definition of the dot product
  • The standard basis vectors
  • The geometry of the dot product
  • Projecting one vector onto another
  • Work (as a physicist uses the term)

Email Subject Line: Math 236 9/24 Your Name

Reading Questions:

1. For an object moving along a path in the plane, why is velocity a vector rather than a scalar?
2. If u and v are unit vectors, give a geometric interpretation of u · v.
3. Let v=(3,4) and w=(5,2). Find the component of v in the w direction.

For September 26

Section 2.4 More on curves and parametrization

• To read: All, but you may de-emphasize the section on conchoids
• Major ideas
  • Using vector tools to study plane curves
  • Rotating, a curve
  • Velocity, speed, and arclength

Email Subject Line: Math 236 9/26 Your Name

Reading Question:

1. Consider the standard sine wave given by the parametrization r(t)=(t, sin(t)) for 0 <= t <= 2*Pi.
   Find a parametrization for the curve obtained by rotating r counterclockwise by Pi/6 radians. (Use can plot on Maple to check your answer.)

For September 29

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