The online book The Geometry of Vector Calculus (aka the Bridge Book) by Tevian Dray and Corinne Manogue is a very good supplemental “text” for our course. While some of the notation is different from that used in Stewart’s Calculus, the explanations in the Bridge Book are very well done.
The correspondence between the sections in Stewart’s Calculus and the Bridge Book:
Stewart’s Calculus  The Bridge Book  
VECTORS AND VECTOR OPERATIONS  
section 12.2: Vectors  Vectors  
section 12.3: The Dot Product  The Dot Product, The Law of Cosines  
section 12.4: The Cross Product  The Cross Product, The Triple Product  
CALCULUS ALONG CURVES  
section 13.2: Derivatives & Integrals of Vector Functions & section 13.4: Motion in Space  Motion in Space  
DERIVATIVES OF MULTIVARIABLE FUNCTIONS  
section 14.1: Functions of Several Variables  Surfaces, Level Sets  
section 14.4: Tangent Planes & Linear Approximations  The Multivariable Differential  
section 14.5: Chain Rule  Chain Rule, Chain Rule via Tree Diagrams  
section 14.6: Directional Derivatives & the Gradient  Gradient, Properties of the Gradient, Product Rules, Directional Derivatives  
section 14.7: Maximum & Minimum Values  Optimization, Curvature and the Second Derivative Test  
section 14.8: Lagrange Multipliers  Lagrange Multipliers  
INTEGRATING MULTIVARIABLE FUNCTIONS  
sections 15.1 & 15.2: Double Integrals  Review of Single Variable Integration, Double Integrals  
section 15.4: Applications of Double Integrals  Mass and Center of Mass  
section 15.6: Triple Integrals  Triple Integrals  
section 15.7: Triple Integrals in Cylindrical Coordinates & 15.8: Triple Integrals in Spherical Coordinates  Curvilinear Coordinates, Triple Integrals in Cylindrical and Spherical Coordinates  
VECTOR CALCULUS  
section 16.1: Vector Fields  Divergence, Curl, Visualizing Divergence and Curl  
section 16.2: Line Integrals  Scalar Line Integrals, Arc Length, Vector Line Integrals, Use What You Know  
section 16.3: Fundamental Theorem for Line Integrals (Conservative Vector Fields)  Independence of Path, Conservative Vector Fields, Finding Potential Functions, Visualizing Conservative Vector Fields  
section 16.4: Green’s Theorem & section 16.8: Stokes’ Theorem  Stokes’ Theorem  
section 16.5: Curl & Divergence  Curl, Divergence  
section 16.6: Parametric Surfaces & section 16.7: Surface Integrals of Vector Fields  Surfaces, General Surface Elements, Activity: Surface Elements on Planes, Cylinders and Spheres, WrapUp: Surface Elements on Planes, Cylinders, and Spheres, Graphs of Functions, Flux, Parametric Surfaces, Scalar Surface Integrals  
section 16.9: Divergence Theorem  The Divergence Theorem 
Other useful sections in The Bridge Book

The Vector Differential: An important section. We will be using the vector differential \(d\boldsymbol{r}\) extensively in this class. The Bridge Book covers this extremely useful object in much greater depth than does Stewart’s Calculus.
 Vector calculus using basis vectors associated to curvilinear coordinates. You will not be responsible for this material in this course, but it may be useful to you in future courses.
 Activity: Curvilinear Basis Vectors
 WrapUp: Curvilinear Basis Vectors
 Orthogonality
 Expressing \(d\vec{\boldsymbol r}\) in Other Coordinate Systems
 Activity: Expressing \(d\vec{\boldsymbol r}\) in Cylindrical and Spherical Coordinates
 WrapUp: Coordinate Expressions for \(d\vec{\boldsymbol r}\)
 The Gradient in Curvilinear Coordinates
 Highly Symmetric Surfaces
 Less Symmetric Surfaces