MA 225
Multivariate Calculus
Section A
Fall 2007

Syllabus
Seb's message about the homework, etc
- Professor Blanchard's addendum related to late or missing assignments
Handouts, etc:
- September 5, 2007
  - Notetaker helper (print out and bring to class)
- September 7, 2007
  - Notetaker helper (print out and bring to class)
- September 10, 2007
  - Notetaker helper (print out and bring to class)
- September 12, 2007
  - Notetaker helper (print out and bring to class)
- September 14, 2007
  - Notetaker helper (print out and bring to class)
- September 17, 2007
  - Notetaker helper (print out and bring to class)
- September 19, 2007
  - Notetaker helper (print out and bring to class)
- September 21, 2007
  - Notetaker helper (print out and bring to class)
- September 24, 2007
  - Notetaker helper (print out and bring to class)
- September 26, 2007
  - Notetaker helper (print out and bring to class)
- September 28, 2007
  - Notetaker helper (print out and bring to class)
- October 1, 2007
  - Notetaker helper (print out and bring to class)
- October 5, 2007
  - Notetaker helper (print out and bring to class)
- October 9, 2007
  - Notetaker helper (print out and bring to class)
- October 10, 2007
  - Notetaker helper (print out and bring to class)
- October 12, 2007
  - Notetaker helper (print out and bring to class)
- October 15, 2007
  - Notetaker helper (print out and bring to class)
- October 17, 2007
  - Notetaker helper (print out and bring to class)
- October 19, 2007
  - Notetaker helper (print out and bring to class)
- October 22, 2007
  - Notetaker helper (print out and bring to class)
- October 24, 2007
  - Notetaker helper (print out and bring to class)
- October 26, 2007
  - Notetaker helper (print out and bring to class)
- October 29, 2007
  - Notetaker helper (print out and bring to class)
- November 2, 2007
  - Notetaker helper (print out and bring to class)
- November 5, 2007
  - Notetaker helper (print out and bring to class)
- November 7, 2007
  - Notetaker helper (print out and bring to class)
- November 9, 2007
  - Notetaker helper (print out and bring to class)
- November 14, 2007
  - Notetaker helper (print out and bring to class)
- November 16, 2007
  - Notetaker helper (print out and bring to class)
- November 19, 2007
  - Notetaker helper (print out and bring to class)
- November 26, 2007
  - Notetaker helper (print out and bring to class)
- November 28, 2007
  - Notetaker helper (print out and bring to class)
- November 30, 2007
  - Notetaker helper (print out and bring to class)
- December 3, 2007
  - Notetaker helper (print out and bring to class)
- December 7, 2007
  - Notetaker helper (print out and bring to class)
- December 10, 2007
  - Notetaker helper (print out and bring to class)
- December 12, 2007
  - Notetaker helper (print out and bring to class)
Homework assignments:
Classroom demos:
- September 5, 2007
  - 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 7, 2007
  - 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 10, 2007
  - Position and direction vectors for a line
  - Animation of parameterized line
  - Two intersecting lines
- September 12, 2007
  - Normal line to a plane
  - Cross product applet from the Syracuse University Physics Department
- September 17, 2007
  - 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 19, 2007
  - 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 21, 2007
  - Animations of three polar curves discussed in class
- September 24, 2007
  - Two animations of area computations in polar coordinates
    (courtesy of Professor Louis Talman, Metropolitan State College of Denver)
- September 26, 2007
  - Many animations of surfaces
    (one courtesy of Professor Selwyn Hollis, Armstrong Atlantic State University,
    one courtesy of Professor Louis Talman, Metropolitan State College of Denver, 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 28, 2007
  - 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 1, 2007
  - Examples of parametrized surfaces
  - Mathematica notebook for parametrized surfaces
- October 5, 2007
  - Various illustrations of level sets
    (one courtesy of Professor John Putz, Alma College)
  - Animation of level sets
    (courtesy of Professor Louis Talman, Metropolitan State College of Denver)
- October 9, 2007
  - Graphs involving certain limits
  - Geometric interpretation of partial derivatives
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
- October 10, 2007
  - Geometric interpretation of partial derivatives
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
- October 12, 2007
  - 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, 2007
  - Type 1 Chain Rule
- October 19, 2007
  - 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 22, 2007
  - Directional derivatives and the gradient
    (courtesy of Professor John Putz, Alma College)
  - Lagrange multipliers
- October 24, 2007
  - Limit of Riemann sums for one-variable integral
    (courtesy of Professor Lawrence Husch, University of Tennessee)
  - Limit of Riemann sums for double integral
- October 26, 2007
  - Limit of Riemann sums for double integral
  - Numerous animations to illustrate interated integration
- October 29, 2007
  - Graphs related to interated integration over rectangles
  - One illustration and one animation related to interated integration over general regions
- November 2, 2007
  - Applet to illustrate area conversion
    (courtesy of Professor Jonathan Rogness, University of Minnesota)
- November 5, 2007
  - Figures to illustrate the computation of surface area
- November 7, 2007
  - Solids to illustrate triple integration
- November 14, 2007
  - Solids to illustrate triple integration using spherical coordinates
- November 16, 2007
  - 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 Duff, Boston University)
  - Demo of electric dipole
    (courtesy of Davidson College webphysics site)
- November 19, 2007
  - Surface whose area can be calculated as a path integral
- November 26, 2007
  - Animation illustrating a line integral
  - Visual estimation of line integrals
- December 3, 2007
  - Streamlines related to electric dipole
    Demo of electric dipole
    (courtesy of Davidson College webphysics site)
- December 7, 2007
  - Curl and divergence
    Curl and divergence demos written by Professor Duane Nykamp, University of Minnesota
- December 10, 2007
  - Flux integral
    Demo of a flux integral written by Professor Duane Nykamp, University of Minnesota
Answers to our exams:
- White exam I
- Yellow exam I
- White exam II
- Yellow exam II
- White exam III (with an additional comment regarding the fence problem)
- Yellow exam III (with an additional comment regarding the fence problem)
Old exams:
- MA 225 exams given in Fall 2005
- MA 225 exams given in Fall 2006 (If this file hangs on page 26, click the reload button.)

MA 225 Multivariate Calculus Section A Fall 2007

MA 225
Multivariate Calculus
Section A
Fall 2007