Double and triple integrals in Cartesian, polar and spherical coordinates. Vector fields and the fundamental theorems of vector calculus developed, line and surface integrals, Green's theorem, ...

Topics include functions of several variables, partial derivatives, the gradient, multiple integrals; introduction to vector-valued functions and vector calculus, divergence, curl, and the integration ...

Higher-order derivatives. Taylor's theorem. Criteria for local minima/maxima. Differential vector calculus: Grad, div, curl. Identities. Levi-Cevita symbol (from 2011). Integration in vector calculus.

The main focus is on developing differential vector calculus, tools for changing coordinate systems and major theorems of integral calculus for functions of more than one variable. This material is ...