Author: Carlos Polanco

Exterior Calculus: Theory and Cases

eBook: US $49 Special Offer (PDF + Printed Copy): US $83
Printed Copy: US $59
Library License: US $196
ISBN: 978-981-4998-79-6 (Print)
ISBN: 978-981-4998-78-9 (Online)
Year of Publication: 2021
DOI: 10.2174/97898149987891210101


Exterior calculus is a branch of mathematics which involves differential geometry. In Exterior calculus the concept of differentiations is generalized to antisymmetric exterior derivatives and the notions of ordinary integration to differentiable manifolds of arbitrary dimensions. It therefore generalizes the fundamental theorem of calculus to Stokes' theorem.

This textbook covers the fundamental requirements of exterior calculus in curricula for college students in mathematics and engineering programs. Chapters start from Heaviside-Gibbs algebra, and progress to different concepts in Grassman algebra. The final section of the book covers applications of exterior calculus with solutions.

Readers will find a concise and clear study of vector calculus and differential geometry, along with several examples and exercises. 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 exterior calculus as part of their college curriculum and equip themselves with the knowledge to apply relevant theoretical concepts in practical situations.


I congratulate Carlos Polanco for his experienced and insightful book Exterior Calculus – Theory and Cases. This work covers profoundly advanced Calculus for a readership that has acquired the necessary mathematical comprehension to direct to geometric algebra. It will guide higher level students as well as their teachers straightforwardly through this topic from Heaviside-Gibbs algebra over Grassmann algebra to differentiation, integration and fundamental theorems of Calculus. Despite the complexity of the subject, this book is written in a highly didactic style, which is reflecting the expertise and the long-term teaching experience of the author at the Universidad Nacional Autónoma de México

The presentation of many examples and case studies as well the solution guide to the chapter exercises at the end of this book will help the readers to deepen and to inspect their acquired knowledge and to relate the theory to practice. I wish that Carlos Polanco’s book will become part of many bookshelves and highly recommend it as a solid and distinctive textbook for advanced courses in Calculus.

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


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