Ebook: Lectures on Clifford (Geometric) Algebras and Applications

Advances in technology over the last 25 years have created a situation in which workers in diverse areas of computerscience and engineering have found it neces­ sary to increase their knowledge of related fields in order to make further progress. Clifford (geometric) algebra offers a unified algebraic framework for the direct expression of the geometric ideas underlying the great mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. Indeed, for many people working in this area, geometric algebra is the natural extension of the real number system to include the concept of direction. The familiar complex numbers of the plane and the quaternions of four dimen­ sions are examples of lower-dimensional geometric algebras. During "The 6th International Conference on Clifford Algebras and their Ap­ plications in Mathematical Physics" held May 20--25, 2002, at Tennessee Tech­ nological University in Cookeville, Tennessee, a Lecture Series on Clifford Ge­ ometric Algebras was presented. Its goal was to to provide beginning graduate students in mathematics and physics and other newcomers to the field with no prior knowledge of Clifford algebras with a bird's eye view of Clifford geometric algebras and their applications. The lectures were given by some of the field's most recognized experts. The enthusiastic response of the more than 80 partici­ pants in the Lecture Series, many of whom were graduate students or postdocs, encouraged us to publish the expanded lectures as chapters in book form.

---

The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird's-eye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field.

Key topics and features of this systematic exposition:

* An Introductory chapter on Clifford Algebras by Pertti Lounesto
* Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups
* John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the well-known complex analysis of the plane to three and higher dimensions
* William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity
* John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and bi-quaternions, have found in computer vision and robotics
* Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry

* Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, on-line calculators, special purpose numeric software, and symbolic add-ons to computer algebra systems

This text will serve beginning graduate students and researchers in diverse areas---mathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications.

---

The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird's-eye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field.

Key topics and features of this systematic exposition:

* An Introductory chapter on Clifford Algebras by Pertti Lounesto
* Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups
* John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the well-known complex analysis of the plane to three and higher dimensions
* William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity
* John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and bi-quaternions, have found in computer vision and robotics
* Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry

* Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, on-line calculators, special purpose numeric software, and symbolic add-ons to computer algebra systems

This text will serve beginning graduate students and researchers in diverse areas---mathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications.

Content:
Front Matter....Pages i-xvii
Introduction to Clifford Algebras....Pages 1-29
Mathematical Structure of Clifford Algebras....Pages 31-52
Clifford Analysis....Pages 53-89
Applications of Clifford Algebras in Physics....Pages 91-133
Clifford Algebras in Engineering....Pages 135-156
Clifford Bundles and Clifford Algebras....Pages 157-188
Back Matter....Pages 189-221

---

The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird's-eye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field.

Key topics and features of this systematic exposition:

* An Introductory chapter on Clifford Algebras by Pertti Lounesto
* Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups
* John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the well-known complex analysis of the plane to three and higher dimensions
* William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity
* John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and bi-quaternions, have found in computer vision and robotics
* Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry

* Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, on-line calculators, special purpose numeric software, and symbolic add-ons to computer algebra systems

This text will serve beginning graduate students and researchers in diverse areas---mathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications.

Content:
Front Matter....Pages i-xvii
Introduction to Clifford Algebras....Pages 1-29
Mathematical Structure of Clifford Algebras....Pages 31-52
Clifford Analysis....Pages 53-89
Applications of Clifford Algebras in Physics....Pages 91-133
Clifford Algebras in Engineering....Pages 135-156
Clifford Bundles and Clifford Algebras....Pages 157-188
Back Matter....Pages 189-221
....