This work provides a systematic examination of derivatives and
integrals of multivariable functions. The approach taken here is
similar to that of the author 's previous text, "Continuous
Functions of Vector Variables": specifically, elementary results
from single-variable calculus are extended to functions in
several-variable Euclidean space. Topics encompass
differentiability, partial derivatives, directional derivatives and
the gradient; curves, surfaces, and vector fields; the inverse and
implicit function theorems; integrability and properties of
integrals; and the theorems of Fubini, Stokes, and Gauss.
Prerequisites include background in linear algebra, one-variable
calculus, and some acquaintance with continuous functions and the
topology of the real line.
Written in a definition-theorem-proof format, the book is
replete with historical comments, questions, and discussions about
strategy, difficulties, and alternate paths. "Derivatives and
Integrals of Multivariable Functions" is a rigorous introduction to
multivariable calculus that will help students build a foundation
for further explorations in analysis and differential geometry.
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