Welcome to
Multivariate Calculus
Paul Blanchard

Geometry

Line with 2 points
Line in space determined by two points
Animation of parameterized line (Quicktime format)
Illustrates sum of position and scalar multiples of direction
Cross product
(courtesy of the Syracuse University Physics Department)
Trefoil knot
Knotted curve given by a vector-valued function
Tangent vector as a limit
Animation to illustrate the limiting process involved in the definition of the derivative
Tangent vector as a limit (Quicktime format)
Animation to illustrate the limiting process involved in the definition of the derivative: control h using the slider
The tangent vector at the point
The derivative vector that results from the above two animations
Tangent vectors from the derivative
The derivative of the elliptical helix as another vector-valued function.
Arc length animation (Quicktime format)
Control of delta t using the slider
Derivative of a curve that sweeps out a trefoil knot
Animation to illustrate the speed at which a point traverses a curve
Area in polar coordinates (Quicktime format)
courtesy of Professor Lou Talman, Metropolitan State College of Denver
Surface of revolution
Another surface of revolution. (Quicktime format)
courtesy of Professor Lou Talman, Metropolitan State College of Denver
Matching question on first exam: Surface A and Surface B

Limit at (0,0) does not exist
graph of 2xy/(x²+y²)
Chain rule animation (Quicktime format)
Directional derivatives and the gradient (Quicktime format)
(courtesy of Professor John Putz, Alma College)
Constrained max/min (Quicktime format)
Animation of constrained max/min for f(x,y) = 2x²+4y² subject to the constraint x²+y²=1