Multivariable Calculus

• Study quadric surfaces as a function of parameter.
• Compare geometry of a transformation with its linear approximation.
• Study roots of polynomials as functions of coefficients.
• Study implicit solution vs their linear approximations.
• Phase plane pictures of gradient vector fields.
• Quality of multivariable Taylor polynomial approximation.
• Behavior of Newton's method and its failures.
• Visualization of three dimensional regions of integration from limits of integration.
• Analyze numerical algorithms with Taylor series computations.
• Lighting models and computer graphics.
• Use Monte Carlo techniques to find the volume of a high dimensional ball.
• Web Resources:

  Mathlab:

  http://www.mathlab.cornell.edu/computer_and_portfolio/index.html#MVAR

  Mathlab Multivariable Calculus in the Lab:

  
  http://www.mathlab.cornell.edu/local_maple/mvc/lecguide.html (Newer Versions in the Maple 7 Folders of the Lab)

  ODES and Multivariable Calculus:

  http://www.geom.umn.edu/ $\tilde{\ }$math335x/Labs/labs.html

  Vector Field Analyzer:

  http://math.la.asu.edu/$\tilde{\ }$kawski