MA 225
Multivariate Calculus
Section A
Fall 2008

Syllabus

Handouts, etc:
 September 3, 2008
 September 5, 2008
 September 8, 2008
 September 10, 2008
 September 12, 2008
 September 15, 2008
 September 17, 2008
 September 19, 2008
 September 22, 2008
 September 24, 2008
 September 26, 2008
 September 29, 2008
 October 1, 2008
 October 6, 2008
 October 8, 2008
 October 10, 2008
 October 14, 2008
 October 15, 2008
 October 17, 2008
 October 20, 2008
 October 22, 2008
 October 24, 2008
 October 27, 2008
 October 29, 2008
 October 31, 2008
 November 3, 2008
 November 7, 2008
 November 10, 2008
 November 12, 2008
 November 14, 2008
 November 17, 2008
 November 19, 2008
 November 21, 2008
 November 24, 2008
 December 1, 2008
 December 5, 2008
 December 8, 2008
 December 10, 2008

Homework assignments:

Homework assigned during the week ending
September 5  Due week of September 8

Homework assigned during the week ending
September 12  Due week of September 15

Homework assigned during the week ending
September 19  Due week of September 22

Homework assigned between September 22
and October 1  Do not submit for grading

Homework assigned during the week ending
October 10  Due week of October 13

Homework assigned during the week ending
October 17  Due week of October 20

Homework assigned during the week ending
October 24  Due week of October 27

Homework assigned during the week ending
October 31  Do not submit for grading

Homework assigned between November 7
and November 14  Due week of November 17

Homework assigned during the week ending
November 21
 Due week of November 24

Homework assigned on
November 24
 Due in CAS/Stone B50
just before Exam III

Homework assigned after Exam III  Do not submit
for grading

Classroom demos:
 September 3, 2008
 Graph of 2x^{2} + y^{2}
 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 vectorvalued function

Circular helix given by a vectorvalued function

Knotted curve given by a vectorvalued 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
vectorvalued function.
 September 17, 2008

Tangent vector at a point on a curve

Derivative of a vectorvalued 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 saddle
 a monkey saddle
 a graph with two critical points
 October 15, 2008
 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
 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

Link to Maxwell's Equations
(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

Answers to our exams:

Old exams: