Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics) (Paperback)

by D. Hestenes (Author), Garret Sobczyk (Author)
Key Phrases: geometric algebra, geometric calculus, simplicial derivative, Directed Integration Theory, The Method of Mobiles, Potential Theory (more...)

Editorial Reviews

Review
`... future authors will owe a great debt to Professors Hestenes and Sobczyk for this pioneering work.' Foundations of Physics, 16, 1986 `I repeat that GC enriches and simplifies everything it touches, not just on an advanced level but also, and perhaps even more so, on an elementary level. I am convinced that GC should be taught to undergraduate in place of the traditional approaches to vector algebra and analysis.' James S. Marsh in American Journal of Physics `If the physics community seizes the opportunity represented by this book, and I hope it does, this book will become the handbook and the bible of GC.' American Journal of Physics, 53:5 (1985)

About the Author
David Hesteness is awarded the Oersted Medal for 2002. The Oersted Award recognizes notable contributions to the teaching of physics. It is the most prestigious award conferred by the American Association of Physics Teachers.

Product Details

• Paperback: 336 pages
• Publisher: Springer; 1 edition (October 24, 2007)
• Language: English
• ISBN-10: 9027725616
• ISBN-13: 978-9027725615
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #664,952 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

59 of 60 people found the following review helpful:

5.0 out of 5 stars a marriage of geometry and algebra made in heaven, January 6, 2003

By	Ananda Himansu (Cleveland, OH United States) - See all my reviews

In 1990, I came across Hestenes' book New Foundations for Classical Mechanics in a university bookstore, and immediately purchased it. In 1999, I finally purchased the paperback version of CA to GC (Kluwer, please keep the paperback in print!). An engineer by training, I was previously only familiar with college vector analysis and with indicial tensor notation. These two books revolutionized my understanding of the algebraic representation of geometric information. Amazon.com now has the "look inside" feature in place for this book, so you can check the table of contents.

Science proceeds both by discovery and by a process of recasting what has been learned in simpler and clearer form. It is the fruits of this latter process that are presented in CA to GC, though some new mathematical results are also introduced. The authors have succeeded admirably in recasting large areas of intermediate to advanced mathematics in a powerful unified algebraic language of exceptional clarity. The authors show how the traditional languages of complex numbers, quaternions, matrices, vectors, tensors, spinors and differential forms are all subsumed by the elegant language of Clifford algebra, and their calculi by Clifford analysis. Quite apart from the pleasure that the clarity of Clifford algebra/analysis affords, its value also lies in making it easier to understand what has already been discovered, and thus extending the mathematical grasp of the human mind. I have often seen the terms "breakthrough" and "groundbreaking" applied to paltry advances in science, mostly by the innovators themselves, but surely Clifford algebra/analysis is deserving of such an appellation. It has been long in gestation, but its time has come.

In CA to GC, the authors present a tour-de-force of mathematical exposition, the writing displaying the same perspicuity and precision that marks all of Hestenes' writing. While further-refined versions of much of the material of the book can now be downloaded in the form of pdf files from Hestenes' website, this book will go down in history as a classic of unifying mathematical exposition. The university student should begin with the New Foundations for Classical Mechanics book, but CA to GC should be read by every mathematician, physicist and engineering scientist. The reader contemplating learning Clifford algebra/analysis should also take a look at the rapidly growing amount of information online, and at other books on the subject. It is an honor for me to be the first reviewer of this book on Amazon.com.

5 of 11 people found the following review helpful:

5.0 out of 5 stars Exact unified language for physics and mathematics, September 23, 2005

By	Omar Leon Sanchez "Omar" (Mexico) - See all my reviews (REAL NAME)

i have been working a few years in geometric calculus and i believe this book should be in every house of every geometrist and every person that is intersted in geometric concepts with physics applications