Author: Carlos Polanco

Advanced Calculus - Fundamentals of Mathematics

eBook: US $69 Special Offer (PDF + Printed Copy): US $117
Printed Copy: US $83
Library License: US $276
ISBN: 978-981-14-1507-4 (Print)
ISBN: 978-981-14-1508-1 (Online)
Year of Publication: 2019
DOI: 10.2174/97898114150811190101


Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations.

This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms.

Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book.

This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.



In his book, Dr. Carlos Polanco elegantly describes fundamentals of Vector Calculus and its applications. The author was able to overcome the usual gap between mathematicians and users, describing the main topics related to Vector Calculus Theory in an easily comprehensible way utilising multiple useful examples and providing exercises. This book can be used as an auxiliary book for students interested in this field as well as a reference book for the seasoned Researcher.

Vladimir N. Uversky
Russian Academy of Sciences
Pushchino, Moscow region, Russia


With Advanced Calculus, Carlos Polanco introduces an experienced view on Vector Calculus that presents a valuable reference for students as well as for their teachers. This book is very well structured, nicely written and provides a comprehensive insight into the complexity of this field. Especially, the presentation of many examples and case studies will help the readers to deepen their acquired knowledge and to relate the theory to practice. It will certainly also help researchers in related fields to refresh their knowledge and to serve as a solid and clear source on Vector Calculus. Rounding up, Carlos Polanco’s book should become part of many bookshelves.

Thomas Buhse
Universidad Autonoma del Estado de Morelos
Cuernavaca Morelos, Mexico