The Vector Calculus Companion, 2e

This companion book contains over 325 worked-out examples of questions commonly seen in a standard collegiate multivariable and vector calculus course. The purpose is to give students extra examples to study, with more depth to the explanations, than might be found in a textbook. Topics covered in this book are the xyz-coordinate axis system, vectors, lines and planes, dot and cross products, projections, multivariable functions and their graphs, domain and range, limits, vector-valued functions, derivatives and integrals, projectile motion, curvature, partial differentiation, directional derivatives and the gradient, unconstrained and constrained optimization, the method of Lagrange multipliers, multivariable integration, polar coordinates, cylindrical and spherical coordinate systems, Jacobians, vector fields, potential functions and gradient vector fields, line integrals (circulation and flux), the Fundamental Theorem of Line Integrals, Green's Theorem, the del operator, divergence and curl, surface integrals and Stokes Theorem.