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

Introduction

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.

Foreword

- Pp. i
Thomas Buhse
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Preface

- Pp. ii
Carlos Polanco*
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Acknowledgements

- Pp. iii
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Dedication

- Pp. iv
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List of Credits

- Pp. v
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List of Symbols

- Pp. vi-viii (3)
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Vector Algebra on R2 and R3

- Pp. 1-13 (13)
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Geometric Algebra on G2

- Pp. 14-30 (17)
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Geometric Algebra on G3

- Pp. 31-47 (17)
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Geometric Algebra on Gn

- Pp. 48-59 (12)
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Differentiation

- Pp. 60-72 (13)
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Integration

- Pp. 73-81 (9)
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Fundamental Theorem of Calculus

- Pp. 82-89 (8)
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Applications

- Pp. 90-96 (7)
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SOLUTIONS

- Pp. 97-117 (21)
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References

- Pp. 118-119 (2)
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Subject Index

- Pp. 120-121 (2)
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