1. Front Matter
Pages i-xiii
2. Antonio Galbis, Manuel Maestre
Pages 1-17
3. Antonio Galbis, Manuel Maestre
Pages 19-72
4. Antonio Galbis, Manuel Maestre
Pages 73-106
5. Antonio Galbis, Manuel Maestre
Pages 107-126
6. Antonio Galbis, Manuel Maestre
Pages 127-145
7. Antonio Galbis, Manuel Maestre
Pages 147-184
8. Antonio Galbis, Manuel Maestre
Pages 185-205
9. Antonio Galbis, Manuel Maestre
Pages 207-267
10. Antonio Galbis, Manuel Maestre
Pages 269-318
11. Antonio Galbis, Manuel Maestre
Pages 319-367
12. Back Matter
Pages 369-375

### Introduction

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.

### Keywords

Stokes' theorem differential form integration on surfaces line integrals orientation of a surface regular k-surfaces surfaces with boundary vector analysis vector calculus vector field

#### Authors and affiliations

• Antonio Galbis
• 1
• Manuel Maestre
• 2
1. 1., Depto. Análisis MatemáticoUniversidad de ValenciaBurjasot (Valencia)Spain
2. 2., Depto. Análisis MatemáticoUniversidad de ValenciaBurjasot (Valencia)Spain

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4614-2200-6