MA 225
Multivariate Calculus
Section A
Fall 2006

Syllabus
Tom's message about the homework, etc
- Professor Blanchard's addendum related to late or missing assignments
Handouts, etc:
- September 6, 2006
  - Notetaker helper (print out and bring to class)
- September 8, 2006
  - Notetaker helper (print out and bring to class)
- September 11, 2006
  - Notetaker helper (print out and bring to class)
- September 13, 2006
  - Notetaker helper (print out and bring to class)
- September 15, 2006
  - Notetaker helper (print out and bring to class)
- September 18, 2006
  - Notetaker helper (print out and bring to class)
- September 20, 2006
  - Notetaker helper (print out and bring to class)
- September 22, 2006
  - Notetaker helper (print out and bring to class)
- September 25, 2006
  - Notetaker helper (print out and bring to class)
- September 27, 2006
  - Notetaker helper (print out and bring to class)
- September 29, 2006
  - Notetaker helper (print out and bring to class)
- October 2, 2006
  - Notetaker helper (print out and bring to class)
- October 6, 2006
  - Notetaker helper (print out and bring to class)
- October 10, 2006
  - Notetaker helper (print out and bring to class)
- October 11, 2006
  - Notetaker helper (print out and bring to class)
- October 13, 2006
  - Notetaker helper (print out and bring to class)
- October 16, 2006
  - Notetaker helper (print out and bring to class)
- October 18, 2006
  - Notetaker helper (print out and bring to class)
- October 20, 2006
  - Notetaker helper (print out and bring to class)
- October 23, 2006
  - Notetaker helper (print out and bring to class)
- October 25, 2006
  - Notetaker helper (print out and bring to class)
- October 27, 2006
  - Notetaker helper (print out and bring to class)
- October 30, 2006
  - Notetaker helper (print out and bring to class)
- November 3, 2006
  - Notetaker helper (print out and bring to class)
- November 6, 2006
  - Notetaker helper (print out and bring to class)
- November 8, 2006
  - Notetaker helper (print out and bring to class)
- November 13, 2006
  - Notetaker helper (print out and bring to class)
- November 15, 2006
  - Notetaker helper (print out and bring to class)
- November 17, 2006
  - Notetaker helper (print out and bring to class)
- November 20, 2006
  - Notetaker helper (print out and bring to class)
- November 27, 2006
  - Notetaker helper (print out and bring to class)
- November 29, 2006
  - Notetaker helper (print out and bring to class)
- December 1, 2006
  - Notetaker helper (print out and bring to class)
- December 4, 2006
  - Notetaker helper (print out and bring to class)
- December 8, 2006
  - Notetaker helper (print out and bring to class)
- December 11, 2006
  - Notetaker helper (print out and bring to class)
Homework assignments:
Classroom demos:
- September 6, 2006
  - Graph of 2x² + y²
  - Tangents for a function of two variables
  - Volumes and Riemann sums
  - Rectangular coordinates of a point
  - Sphere (courtesy of Professor Selwyn Hollis, Armstrong Atlantic State University)
- September 8, 2006
  - 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 11, 2006
  - Position and direction vectors for a line
  - Animation of parameterized line
  - Two intersecting lines
- September 13, 2006
  - Normal line to a plane
  - Cross product applet from the Syracuse University Physics Department
- September 18, 2006
  - 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 20, 2006
  - 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 22, 2006
  - Animations of three polar curves discussed in class
- September 25, 2006
  - Two animations of area computations in polar coordinates
    (courtesy of Professor Lou Talman, Metropolitan State College of Denver)
- September 27, 2006
  - Many animations of surfaces
    (one courtesy of Professor Selwyn Hollis, Armstrong Atlantic State University and
    five courtesy of Professor John Putz, Alma College)
  - Interactive Gallery of Quadric Surfaces
    courtesy of Professor Jonathan Rogness of the University of Minnesota
- September 29, 2006
  - 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
- October 2, 2006
  - Examples of parametrized surfaces
  - Mathematica notebook for parametrized surfaces
- October 6, 2006
  - Various illustrations of level sets
    (one courtesy of Professor John Putz, Alma College)
  - Animation of level sets
    (courtesy of Professor Lou Talman, Metropolitan State College of Denver)
- October 10, 2006
  - Graphs involving certain limits
  - Geometric interpretation of partial derivatives
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
- October 11, 2006
  - Geometric interpretation of partial derivatives
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
- October 13, 2006
  - 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 16, 2006
  - Type 1 Chain Rule
- October 18, 2006
  - 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 20, 2006
  - 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 23, 2006
  - Lagrange multipliers
- October 25, 2006
  - Limit of Riemann sums for one-variable integral
    (courtesy of Professor Lawrence Husch, University of Tennessee)
  - Limit of Riemann sums for double integral
- October 27, 2006
  - Numerous animations to illustrate interated integration
- October 30, 2006
  - One illustration and one animation related to interated integration over general regions
- November 3, 2006
  - Applet to illustrate area conversion
    Area conversion applet written by Professor Jonathan Rogness, University of Minnesota
- November 6, 2006
  - Figures to illustrate the computation of surface area
- November 8, 2006
  - Solids to illustrate triple integration
- November 13, 2006
  - Solids to illustrate triple integration using spherical coordinates
- November 15, 2006
  - Link to Maxwell's Equations
  - Velocity field for wind currents in San Francisco Bay
  - Demo of electric dipole
- November 20, 2006
  - Surface whose area can be calculated as a path integral
- November 27, 2006
  - Animation illustrating a line integral
  - Visual estimation of line integrals
- December 4, 2006
  - Curl and divergence
    Curl and divergence demos written by Professor Duane Nykamp, University of Minnesota
Answers to our exams:
Old exams:
- MA 225 exams given in Spring 2001
- MA 225 exams given last fall

MA 225 Multivariate Calculus Section A Fall 2006

MA 225
Multivariate Calculus
Section A
Fall 2006