The links below contain review material for an undergraduate-level course on multivariable calculus. The content is based on MATH 13 at Tufts University and follows closely the text of *Calculus – Early Transcendentals *by Briggs and Cochran.

Chapter 11 – Vectors and Vector-Valued Functions

Includes:

11.1 – Vectors in the Plane, 11.2 – Vectors in Three Dimensions, 11.3 – Dot Products, 11.4 – Cross Products, 11.5 – Lines and Curves in Space, 11.6 – Calculus of Vector-Valued Functions, 11.7 – Motion in Space, and 11.8 – Length of Curves

Chapter 12 – Functions of Several Variables

Includes:

12.1 – Planes and Surfaces, 12.2 – Graphs and Level Curves, 12.4 – Partial Derivatives, 12.5 – The Chain Rule, 12.6 – Directional Derivatives and the Gradient, 12.7 – Tangent Planes and Linear Approximations, 12.8 – Maximum/Minimum Problems, 12.9 – Lagrange Multipliers

Chapter 13 – Multiple Integration

Includes:

13.1 – Double Integrals over Rectangular Regions, 13.2 – Double Integrals over General Regions, 13.3 – Double Integrals in Polar Coordinates, 13.4 – Triple Integrals, 13.5 – Triple Integrals in Cylindrical and Spherical Coordinates

Chapter 14, Part I – Vector Fields

Includes:

14.1 – Vector Fields and Integrals, 14.2 – Line Integrals, 14.3 – Conservative Fields

Chapter 14, Part II – Vector Calculus – Part II

Includes:

14.4 – Green’s Theorem, 14.5 – Divergence and Curl, 14.6 – Surface Integrals, 14.7 – Stokes’ Theorem, 14.8 – Divergence Theorem

There is also an excellent Calc III review sheet made by a friend of mine from the University of Connecticut, which I have also included here.