General Mathematics II

Parametric equations and polar coordinates
Parametric representation of curves on the plane, calculus with parametric curves, polar coordinates, graphic representation of functions, areas and lengths or curves, conic sections. [1.5 weeks]
Vectors and the geometry of space
Coordinate systems in three dimensions, vectors, scalar and vector product, lines and planes, cylinders and surfaces of second order [1.5 weeks]
Vector functions and movement in space
Curves in space, integrals of vector functions, length of an arc, curvature and normal vectors of a curve, velocity and acceleration. [1 week]
Partial derivatives
Functions of many variables, limits, continuity, partial derivatives, chain rule, directional derivatives, gradient, tangent planes, extrema and saddle points, Lagrange multipliers, Taylor expansion, functions with constrained variables. [2 weeks]
Multiple integrals
Double and triple integrals and applications [3 weeks]
Integrals and vector fields
Line integrals, vector fields, work, circulation, flux, conservative fields, Green’s theorem on the plane, surface integrals, Stokes theorem, divergence theorem. [3 weeks]
Course review and in class problems
[1 week]