Antonio Galbis & Manuel Maestre 
Vector Analysis Versus Vector Calculus 

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.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, and 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.

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Preface.- 1 Vectors and Vector Fields.- 2 Line Integrals.- 3 Regular k-surfaces.- 4 Flux of a Vector Field.- 5 Orientation of a Surface.- 6 Differential Forms.- Integration on Surfaces.- 8 Surfaces with Boundary.- 9 The General Stokes’ Theorem.- Solved Exercises.- References.- Index

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Antonio Galbis and Manuel Maestre are currently professors of mathematics at the University of Valencia in Spain.