Functions of Several Variables

Unit I: Vector functions and space curves, Arc length and curvature, Motion in space, Cylindrical and spherical coordinates.

Unit II: Partial derivatives, Taylor series expansion in two variables, Tangent planes and differentials, The chain rule, Directional derivatives and the gradient vector, Total derivative, Local and absolute extrema for functions of several variables.

Unit III: Double and iterated integrals including polar coordinates, Applications of double integrals, Triple and iterated integrals, including cylindrical and spherical coordinates, Change of variable in multiple integrals.

Unit IV: Vector fields and line integrals, The fundamental theorem for line integrals, Curl and divergence, Green’s theorem, Stokes’ theorem, Divergence theorem.