MA 225
Multivariate Calculus
Section A
Fall 2005

Final exam, homework grades, and final course grades (via CourseInfo)
Syllabus
Tiffany's message about the homework, etc
- Professor Blanchard's addendum related to late or missing assignments
Handouts, etc:
- September 7, 2005
  - Notetaker helper (print out and bring to class)
- September 9, 2005
  - Notetaker helper (print out and bring to class)
- September 12, 2005
  - Notetaker helper (print out and bring to class)
- September 14, 2005
  - Notetaker helper (print out and bring to class)
- September 16, 2005
  - Notetaker helper (print out and bring to class)
- September 19, 2005
  - Notetaker helper (print out and bring to class)
- September 21, 2005
  - Notetaker helper (print out and bring to class)
- September 23, 2005
  - Notetaker helper (print out and bring to class)
- September 26, 2005
  - Notetaker helper (print out and bring to class)
- September 30, 2005
  - Notetaker helper (print out and bring to class)
- October 3, 2005
  - Notetaker helper (print out and bring to class)
- October 5, 2005
  - Notetaker helper (print out and bring to class)
- October 7, 2005
  - Notetaker helper (print out and bring to class)
- October 12, 2005
  - Notetaker helper (print out and bring to class)
- October 14, 2005
  - Notetaker helper (print out and bring to class)
- October 17, 2005
  - Notetaker helper (print out and bring to class)
- October 19, 2005
  - Notetaker helper (print out and bring to class)
- October 21, 2005
  - Notetaker helper (print out and bring to class)
- October 24, 2005
  - Notetaker helper (print out and bring to class)
- October 26, 2005
  - Notetaker helper (print out and bring to class)
- October 28, 2005
  - Notetaker helper (print out and bring to class)
- October 31, 2005
  - Notetaker helper (print out and bring to class)
- November 4, 2005
  - Notetaker helper (print out and bring to class)
- November 7, 2005
  - Notetaker helper (print out and bring to class)
- November 9, 2005
  - Notetaker helper (print out and bring to class)
- November 14, 2005
  - Notetaker helper (print out and bring to class)
- November 16, 2005
  - Notetaker helper (print out and bring to class)
- November 18, 2005
  - Notetaker helper (print out and bring to class)
- November 21, 2005
  - Notetaker helper (print out and bring to class)
- November 28, 2005
  - Notetaker helper (print out and bring to class)
- November 30, 2005
  - Notetaker helper (print out and bring to class)
- December 2, 2005
  - Notetaker helper (print out and bring to class)
- December 5, 2005
  - Notetaker helper (print out and bring to class)
- December 7, 2005
  - Notetaker helper (print out and bring to class)
- December 9, 2005
  - Notetaker helper (print out and bring to class)
Homework assignments:
Classroom demos:
- September 7, 2005
  - Graph of 2x² + y²
  - Tangents for a function of two variables
  - Volumes and Riemann sums
  - Rectangular coordinates of a point
- September 9, 2005
  - 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 12, 2005
  - Position and direction vectors for a line
  - Animation of parameterized line
  - Two intersecting lines
- September 14, 2005
  - Normal line to a plane
  - Cross product applet from the Syracuse University Physics Department
- September 19, 2005
  - 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 Leathrum at 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 21, 2005
  - 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 23, 2005
  - Animations of three polar curves discussed in class
- September 26, 2005
  - Two animations of area computations in polar coordinates
    (courtesy of Professor Lou Talman, Metropolitan State College of Denver)
- September 30, 2005
  - Many examples of surfaces
  - Many animations of surfaces
    (one courtesy of Professor Selwyn Hollis, Armstrong Atlantic State University and
    five courtesy of Professor John Putz, Alma College)
- October 3, 2005
  - Examples of parameterized surfaces
  - Mathematica notebook for parameterized surfaces
- October 5, 2005
  - Various illustrations of level sets
    (one courtesy of Professor John Putz, Alma College)
- October 7, 2005
  - Animation of level sets
    (courtesy of Professor Lou Talman, Metropolitan State College of Denver)
  - Graphs involving certain limits
  - Geometric interpretation of partial derivatives
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
- October 12, 2005
  - Geometric interpretation of partial derivatives
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
  - Example where mixed partials are not equal
    (courtesy of Professor Tom Vogel of Texas A&M University)
- October 14, 2005
  Various graphs related to questions of extrema including:
  - a maximum
  - a saddle
  - a monkey saddle
  - a graph with two critical points
- October 17, 2005
  - Type 1 Chain Rule
- October 19, 2005
  - Directional derivatives and the gradient
    (courtesy of Professor John Putz, Alma College)
- October 21, 2005
  - Directional derivatives and the gradient
    (courtesy of Professor John Putz, Alma College)
  - Directional derivatives and the gradient
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
- October 24, 2005
  - Lagrange multipliers
- October 26, 2005
  - Limit of Riemann sums for one-variable integral
    (courtesy of Professor Lawrence Husch, University of Tennessee)
  - Limit of Riemann sums for double integral
- October 28, 2005
  - Numerous animations to illustrate interated integration
- October 31, 2005
  - One illustration and one animation related to interated integration over general regions
- November 4, 2005
  - Applet to illustrate area conversion
    Area conversion applet written by Professor Jonathan Rogness, University of Minnesota
- November 7, 2005
  - Figures to illustrate the computation of surface area
- November 9, 2005
  - One surface to illustrate the computation of surface area
  - Solids to illustrate triple integration
- November 14, 2005
  - Solids to illustrate triple integration
- November 16, 2005
  - Solids to illustrate triple integration using spherical coordinates
- November 18, 2005
  - Link to Maxwell's Equations
  - Velocity field for wind currents in San Francisco Bay
  - Demo of electric dipole
- November 21, 2005
  - Surface whose area can be calculated as a path integral
- November 28, 2005
  - Animation illustrating a line integral
  - Visual estimation of line integrals
- December 5, 2005
  - Curl and divergence
    Curl and divergence demos written by Professor Duane Nykamp, University of Minnesota
Frequently asked questions (FAQ)
- How do I get handouts from the computer?
- How do I play the Quicktime animations?
Homework cover sheet
Answers to our exams:
Old exams:
- MA 225 exams given in Spring 2001 (MWF class)
- MA 225 exams given in Fall 2001 (TR class)

MA 225 Multivariate Calculus Section A Fall 2005

MA 225
Multivariate Calculus
Section A
Fall 2005