Chapter 1 Multivariable Spaces and Functions
1.1 Euclidean Space
1.1.1 Exercises
1.2 Rn as a Vector Space
1.2.1 Exercises
1.3 Dot Product, Angles & Projection
1.3.1 Exercises
1.4 Lines, Planes, and Hyperplanes
1.4.1 Exercises
1.5 The Cross Product
1.5.1 Exercises
1.6 Functions of a Single Variable
1.6.1 Exercises
1.7 Multivariable Functions
1.7.1 Exercises
1.8 Graphing Surfaces
1.8.1 Exercises

Chapter 2 Multivariable Derivatives
2.1 Partial Derivatives
2.1.1 Exercises
2.2 The Total Derivative
2.2.1 Exercises
2.3 Linear Approximation, Tangent Planes, and the Differential
2.3.1 Exercises
2.4 Differentiation Rules
2.4.1 Exercises
2.5 The Directional Derivative
2.5.1 Exercises
2.6 Change of Coordinates
2.6.1 Exercises
2.7 Level Sets & Gradient Vectors
2.7.1 Exercises
2.8 Parameterizing Surfaces
2.8.1 Exercises
2.9 Local Extrema
2.9.1 Exercises
2.10 Optimization
2.10.1 Exercises
2.11 Lagrange Multipliers
2.11.1 Exercises
2.12 Implicit Differentiation
2.12.1 Exercises
2.13 Multivariable Taylor Polynomials & Series
2.13.1 Exercises

Chapter 3 Multivariable Integrals
3.1 Iterated Integrals
3.1.1 Exercises
3.2 Integration in R2
3.2.1 Exercises
3.3 Polar Coordinates
3.3.1 Exercises
3.4 Integration in R3 and Rn
3.4.1 Exercises
3.5 Volume
3.5.1 Exercises
3.6 Cylindrical and Spherical Coordinates
3.6.1 Exercises
3.7 Average Value
3.7.1 Exercises
3.8 Density & Mass
3.8.1 Exercises
3.9 Centers of Mass
3.9.1 Exercises
3.10 Moments of Inertia
3.10.1 Exercises
3.11 Surfaces and Area
3.11.1 Exercises

Chapter 4 Integration and Vector Fields
4.1 Vector Fields
4.1.1 Exercises
4.2 Line Integrals
4.2.1 Exercises
4.3 Conservative Vector Fields
4.3.1 Exercises
4.4 Green's Theorem
4.4.1 Exercises
4.5 Flux through a Surface
4.5.1 Exercises
4.6 The Divergence Theorem
4.6.1 Exercises
4.7 Stokes' Theorem
4.7.1 Exercises