Multivariable Calculus Set Free: Infinitesimals Ride Again

A sequel to the author's previous book, Calculus Set Free: Infinitesimals to the Rescue, this text explores all the key topics of multivariable calculus using infinitesimal methods.These recently developed infinitesimal procedures, based on the approximation relation, simplify limit-based computations and make many concepts more intuitive and accessible. Limit-based computations utilize infinitesimals, simplifying computations and making a wider variety of limits accessible.Definitions of double integrals, triple integrals, line integrals, and surface integrals, as well as related geometric and physical applications, are based on infinitely many subintervals (or subregions) of infinitesimal size, resulting more clearly in a sum and simplifying definitions.Local linearity is captured in an easily understood approximation formula, demystifying the use of straight objects instead of curved objects when developing integration formulas.Throughout the text, abundant use of diagrams aids the