The text treats a number of topics often not included in "Calc 3" texts:

Partial Derivatives in Thermodynamics

Second Order Constrained Derivatives

Visualization of the Osculating Circle and Sphere

Visualization of Surface Curvature

Linearization of the Pendulum

Animations of Flows

Functional Dependence and Applications

Local and Global Vector Potentials

It also treats a few topics using advanced features of Mathematica

Non-elementary formulas: 

The period of the nonlinear pendulum

The normal (or Gaussian) statistical integral

The inverse of x^x.

Difficult, but concrete computations:

Critical point conditions in higher dimensions: Mathematica computes eigenvalues 

The distance between surfaces as a constrained 6D MAX-min problem with bordered hessians