Calculus and Analytic Geometry III

Catalog description

Topics include differentiation of vectors, space curves and curvature, functions of variables, level curves and surfaces, limits and continuity, partial derivatives, total differential, tangent planes, gradient operator, the directional derivative, multivariable forms of the chain rule, locating (maxima, minima, saddle points), the method of Lagrange multipliers, multiple integrals (in rectangular, polar, cylindrical and spherical coordinates), transformations of multiple integrals and the Jacobian, surface area, applications of multiple integrals to geometry and mechanics, line integrals (two and three dimensions), vector fields, circulation and flux in two dimensions, and Green's Theorem.