# MA 225 Multivariate Calculus Section A Fall 2008

• Syllabus

• Handouts, etc:

• Homework assignments:

• Classroom demos:
• September 3, 2008
• Graph of 2x2 + y2
• Tangents for a function of two variables
• Volumes and Riemann sums
• Rectangular coordinates of a point
• September 5, 2008
• Position vector
• Line in space determined by two points
• Position and direction vectors for a line
• Animation of parameterized line
• Vector form of line in the plane
• September 8, 2008
• Position and direction vectors for a line
• Animation of parameterized line
• Two intersecting lines
• September 10, 2008
• Normal line to a plane
• Cross product applet from the Syracuse University Physics Department
• September 15, 2008
• Line swept out as the values of a vector-valued function
• Circular helix given by a vector-valued function
• Knotted curve given by a vector-valued function
• Graphing applet written by Professor Tom Leathrum, Jacksonville State University
• Elliptical helix in space with a point on it
• Animation to illustrate the limiting process involved in the definition of the derivative
• Animation to illustrate the limiting process involved in the definition of the derivative: control h using the slider
• The derivative vector that results from the above two animations
• The derivative of the elliptical helix as another vector-valued function.
• September 17, 2008
• Tangent vector at a point on a curve
• Derivative of a vector-valued function
• Arc length animation(s)
• Derivative of the curve that sweeps out the trefoil knot
• September 19, 2008
• Animations of three polar curves discussed in class
• September 22, 2008
• Two animations of area computations in polar coordinates
(courtesy of Professor Louis Talman, Metropolitan State College of Denver)
• September 24, 2008
• Many examples of surfaces
• Interactive Gallery of Quadric Surfaces
courtesy of Professor Jonathan Rogness of the University of Minnesota
• September 26, 2008
• Many animations of quadric surfaces
(five courtesy of Professor John Putz, Alma College)
• Interactive Gallery of Quadric Surfaces
courtesy of Professor Jonathan Rogness of the University of Minnesota
• Parametric surface graphing applet
courtesy of Professor Tom Leathrum, Jacksonville State University
• September 29, 2008
• Examples of parametrized surfaces
• Mathematica notebook for parametrized surfaces
• October 1, 2008
• Various illustrations of level sets
(one courtesy of Professor John Putz, Alma College)
• October 6, 2008
• Graphs involving certain limits
• Geometric interpretation of partial derivatives
(courtesy of Professor Jonathan Rogness, University of Minnesota)
• October 8, 2008
• Geometric interpretation of partial derivatives
(courtesy of Professor Jonathan Rogness, University of Minnesota)
• October 10, 2008
• Example where mixed partials are not equal
(courtesy of Professor Tom Vogel of Texas A&M University)
• Various graphs related to questions of extrema including:
• a maximum
• a graph with two critical points
• October 15, 2008
• Type 1 Chain Rule
• October 17, 2008
• Directional derivatives and the gradient
(courtesy of Professor Jonathan Rogness, University of Minnesota)
• October 20, 2008
• Directional derivatives and the gradient
(courtesy of Professor John Putz, Alma College)
• October 22, 2008
• Lagrange multipliers
• October 24, 2008
• Limit of Riemann sums for double integral
• October 27, 2008
• Numerous animations to illustrate iterated integration
• October 29, 2008
• Two illustrations and one animation related to interated integration over general regions
• October 31, 2008
• Applet to illustrate area conversion
(courtesy of Professor Jonathan Rogness, University of Minnesota)
• November 3, 2008
• Figures to illustrate the computation of surface area
• November 7, 2008
• Solids to illustrate triple integration
• November 12, 2008
• Solids to illustrate triple integration using spherical coordinates
• November 14, 2008
(courtesy of the HyperPhysics web site at Georgia State University)
• Velocity field for wind currents in San Francisco Bay
(courtesy of SFPORTS)
• Demo of gravitational field of the Earth
(courtesy of Professor Andrew Duffy, Boston University)
• Demo of electric dipole
(courtesy of Professor Andrew Duffy, Boston University)
• November 17, 2008
• Surface whose area can be calculated as a path integral
• November 19, 2008
• Animation illustrating a line integral
• Visual estimation of line integrals
• December 5, 2008
• Curl and divergence
Curl and divergence demos written by Professor Duane Nykamp, University of Minnesota
• December 10, 2008
• Flux integrals
Demo of a flux integral written by Professor Duane Nykamp, University of Minnesota
• Surface for the example presented in class