Math 10C - Spring 2001
Links to Web Sites with Graphical Demonstrations

Chapter 9.3-9.4: Vectors

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

Chapter 10.1: Graphs of multivariable functions

• 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).
• Current wind conditions, national map (Agriculture Online)
  This is another vector field.
• Topographic maps of the United States, and a topographic map of Del Mar/La Jolla/UCSD (TopoZone)
  These are contour maps.
• 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.

Chapter 10.4: Tangent plane, approximations

• 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 10.5.1: Chain rule for functions of two variables

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

Chapter 10.5.5: 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).

Cross Product

• Java applet illustrating the cross product in 3D (B. Surendranath Reddy; Hyderabad, India),
  and another such applet (David McNamara, Alan Middleton, Eric Schiff; Syracuse University).
• Course notes about the cross product (Elizabeth Wood; Clinton Community College, Iowa)
  and more course notes (David Johnson; Lehigh University).