
 Mathematical Sciences, Undergraduate Course Descriptions 
  Taylor's Theorem; geometric sequences and series and their applications in finance; vectors and matrices, lines, and planes; partial derivatives, directional derivatives, gradient, chain rule, maximumminimum problems, Lagrange multipliers and the KuhnTucker Theorem. 
  Vectors, lines, planes, quadratic surfaces, polar, cylindrical and spherical coordinates, partial derivatives, directional derivatives, gradient, divergence, curl, chain rule, maximumminimum problems, multiple integrals, parametric surfaces and curves, line integrals, surface integrals, GreenGauss theorems. 
  Vector spaces: subspaces and linear independence, basis and dimension, row equivalence of matrices, general theorems about vector spaces, systems of linear equations, linear manifolds. 
 www.math.cmu.edu /ug/courses/coursesdesc.html (2856 words) 
