Welcome to
MA 225 Multivariate Calculus
Section A
Paul Blanchard
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.
Area in polar coordinates
(
Quicktime format
)
(courtesy of Professor Lou Talman, Metropolitan State College of Denver)
Unit sphere
(
Quicktime format
)
(courtesy of Professor Selwyn Hollis, Armstrong Atlantic State University)
Surface of revolution
Limit at (0,0) does not exist
graph of 2xy/(x
^{2}
+y
^{2}
)
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) = 2x
^{2}
+4y
^{2}
subject to the constraint x
^{2}
+y
^{2}
=1
Riemann sums
converging to the integral (
Quicktime format
)
an animation of
many y-slices
(
Quicktime format
)
Applet to illustrate area conversion
Area conversion applet written by Professor Leathrum at Jacksonville State University
A "cube" in space determined by spherical coordinates
40 different spherical "cubes"
Vector fields (pdf format)
involved in the Problem of the Day
Line integral
animation (
Quicktime format
)