- Use various tests to determine series convergence, perform standard operations with convergent power series, find Taylor and Maclaurin representations.
- Handle vectors fluently in solving problems involving the geometry of lines, curves, planes, and surfaces in space.
- Examine functions of several variables, define and compute limits of functions at points and define and determine continuity
- Define and compute partial derivatives, directional derivatives and differentials of multivariable functions and examine conditions of differentiability; find the equation of the tangent plane to a surface at a point.
- Find local extreme values of functions of several variables, test for saddle points, examine the conditions for the existence of absolute extreme values, solve constraint problems using Lagrange multipliers, and solve related application problems.
Use Rectangular, Cylindrical and Spherical Coordinates Systems to define space curves and surfaces in Cartesian and Parametric forms
Integrate functions of several variables
Examine vector fields and define and evaluate line integrals using the Fundamental Theorem of line integrals and Green’s Theorem; compute arc length
Define and compute the Curl and Divergence of vector fields and apply Green’s Theorem to evaluate line integrals, surface integrals and flux integrals