The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text
takes a differential geometric point of view and provides for the student a bridge between pure
and applied mathematics by carefully building a formal rigorous development of the topic and
following this through to concrete applications in two and three variables. Several practical
methods and many solved exercises are provided. This book tries to show that vector analysis
and vector calculus are not always at odds with one another. Key topics include: - vectors and
vector fields - line integrals - regular k-surfaces - flux of a vector field - orientation of a
surface - differential forms - Stokes' theorem - divergence theorem. This book is intended for
upper undergraduate students who have completed a standard introduction to differential and
integral calculus for functions of several variables. The book can also be useful to
engineering and physics students who know how to handle the theorems of Green Stokes and Gauss
but would like to explore the topic further.ully building a formal rigorous development of the
topic and following this through to concrete applications in two and three variables. Several
practical methods and many solved exercises are provided. This book tries to show that vector
analysis and vector calculus are not always at odds with one another. Key topics include: -
vectors and vector fields - line integrals - regular k-surfaces - flux of a vector field -
orientation of a surface - differential forms - Stokes' theorem - divergence theorem. This book
is intended for upper undergraduate students who have completed a standard introduction to
differential and integra
