MA 225
Multivariate Calculus
Section A
Fall 2008

Final exam, homework grades, and final course grades (via blackboard.bu.edu)
Syllabus
Handouts, etc:
- September 3, 2008
  - Notetaker helper (print out and bring to class)
- September 5, 2008
  - Notetaker helper (print out and bring to class)
- September 8, 2008
  - Notetaker helper (print out and bring to class)
- September 10, 2008
  - Notetaker helper (print out and bring to class)
- September 12, 2008
  - Notetaker helper (print out and bring to class)
- September 15, 2008
  - Notetaker helper (print out and bring to class)
- September 17, 2008
  - Notetaker helper (print out and bring to class)
- September 19, 2008
  - Notetaker helper (print out and bring to class)
- September 22, 2008
  - Notetaker helper (print out and bring to class)
- September 24, 2008
  - Notetaker helper (print out and bring to class)
- September 26, 2008
  - Notetaker helper (print out and bring to class)
- September 29, 2008
  - Notetaker helper (print out and bring to class)
- October 1, 2008
  - Notetaker helper (print out and bring to class)
- October 6, 2008
  - Notetaker helper (print out and bring to class)
- October 8, 2008
  - Notetaker helper (print out and bring to class)
- October 10, 2008
  - Notetaker helper (print out and bring to class)
- October 14, 2008
  - Notetaker helper (print out and bring to class)
- October 15, 2008
  - Notetaker helper (print out and bring to class)
- October 17, 2008
  - Notetaker helper (print out and bring to class)
- October 20, 2008
  - Notetaker helper (print out and bring to class)
- October 22, 2008
  - Notetaker helper (print out and bring to class)
- October 24, 2008
  - Notetaker helper (print out and bring to class)
- October 27, 2008
  - Notetaker helper (print out and bring to class)
- October 29, 2008
  - Notetaker helper (print out and bring to class)
- October 31, 2008
  - Notetaker helper (print out and bring to class)
- November 3, 2008
  - Notetaker helper (print out and bring to class)
- November 7, 2008
  - Notetaker helper (print out and bring to class)
  - Answer to problem in the notetaker helper
- November 10, 2008
  - Notetaker helper (print out and bring to class)
- November 12, 2008
  - Notetaker helper (print out and bring to class)
- November 14, 2008
  - Notetaker helper (print out and bring to class)
- November 17, 2008
  - Notetaker helper (print out and bring to class)
- November 19, 2008
  - Notetaker helper (print out and bring to class)
- November 21, 2008
  - Notetaker helper (print out and bring to class)
- November 24, 2008
  - Notetaker helper (print out and bring to class)
- December 1, 2008
  - Notetaker helper (print out and bring to class)
- December 5, 2008
  - Notetaker helper (print out and bring to class)
- December 8, 2008
  - Notetaker helper (print out and bring to class)
- December 10, 2008
  - Notetaker helper (print out and bring to class)
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
  - Sphere (courtesy of Professor Selwyn Hollis, Armstrong Atlantic State University)
- 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
    (one courtesy of Professor Selwyn Hollis, Armstrong Atlantic State University)
  - 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
  - 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
  - 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:
- MA 225 exams given in Fall 2006 (If this file hangs on page 26, click the reload button.)
- MA 225 exams given in Fall 2007

MA 225 Multivariate Calculus Section A Fall 2008

MA 225
Multivariate Calculus
Section A
Fall 2008