Introduction

Abstract

We wrote this book as a supplement for the third semester of a physical science or engineering calculus sequence. It can equally well be used in a postcalculus course or problem seminar on mathematical methods for scientists and engineers. The subject is traditionally called Calculus of Several Variables, Vector Calculus, or Multivariable Calculus. The usual content is:

• Preliminary Theory of Vectors: Dot and Cross Products; Vectors, Lines, and Planes in R³.

• Vector-Valued Functions: Derivatives and Integrals of Vector-Valued Functions of One Variable; Space Curves; Tangents and Normals; Arclength and Curvature.

• Partial Derivatives: Directional Derivatives; Gradients; Surfaces; Tangent Planes; Multivariable Max/Min Problems; Lagrange Multipliers.

• Multiple Integrals: Double and Triple Integrals; Cylindrical and Spherical Coordinates; Change of Variables.

• Calculus of Vector Fields: Line and Surface Integrals; Fundamental Theorem of Line Integrals; Green’s, Stokes’, and Divergence Theorems.