Chapter 11.4: Areas in polar coordinates

• Area of one band of a spiral

Chapter 12.1-12.2: Vector arithmetic

• Java applet: Adding vectors in 2D and 3D (Fu-Kwun Hwang, National Taiwan Normal University)
• Java applet: Adding and subtracting vectors in 2D (Paul Flavin)

Chapter 12.3: Dot Product

• Java applet: dot product (Paul Falstad)

Chapter 12.4: Cross Product

• Java applet illustrating the cross product in 3D (David McNamara, Alan Middleton, Eric Schiff; Syracuse University).

Chapter 14: Partial derivatives, tangent planes, approximations

• Vector fields:
  San Fransisco Bay Wind Patterns (US Geological Survey)
  This is a plot of a vector field (a function with 2 inputs (x,y), and a 2D vector as output).
• Topographic maps:
  • Back Country Maps. For UCSD, at the bottom left enter Lat: 32.87694, Lon: -117.24 and hit Submit. Then zoom in and hit Topo.
  • A topographic map plugin for Google Earth: download Google Earth and the USA topographic map plugin for it.
  • National Geographic's TOPO!
• Weather maps (temperature, pressure, etc.):
  • The Weather Channel (using color coding for temperature instead of contours)
  • weatherforyou.com (using contours for pressure)
• Plot of z = x y², made with MATLAB.
  This shows a 3D graph and its conversion to a contour map, superimposed in the same diagram.
• Java 3d Visualizer (Paul Flavin)
  Animates a number of 3D objects, each built up from small 2D polygons.
• Approximating a 3D object by patching together lots of small 2D polygons, made with MATLAB.

Chapter 14.5: Chain rule for functions of two variables

• Contour map description of chain rule, made with MATLAB.

Chapter 14.7: Maxima and Minima for functions of two variables

• Saddle point illustration made with MATLAB.
  This is a plot of z=xy, with a saddle point at (x,y)=(0,0).

Other links

• Trigonometry review (David E. Joyce; Clark University)
• S.O.S. Mathematics - math review material