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Clifford Algebra to Geometric Calculus : A Unified Language for Mathematics and Physics :  A Unified Language for Mathematics and Physics - David Hestenes

Clifford Algebra to Geometric Calculus : A Unified Language for Mathematics and Physics

A Unified Language for Mathematics and Physics

Paperback Published: August 1987
ISBN: 9789027725615
Number Of Pages: 314

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` ... 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)

`... 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)

1 / Geometric Algebra.- 1-1. Axioms, Definitions and Identities.- 1-2. Vector Spaces, Pseudoscalars and Projections.- 1-3. Frames and Matrices.- 1-4. Alternating Forms and Determinants.- 1-5. Geometric Algebras of PseudoEuclidean Spaces.- 2 / Differentiation.- 2-1. Differentiation by Vectors.- 2-2. Multivector Derivative, Differential and Adjoints.- 2-3. Factorization and Simplicial Derivatives.- 3 / Linear and Multilinear Functions.- 3-1. Linear Transformations and Outermorphisms.- 3-2. Characteristic Multivectors and the Cayley-Hamilton Theorem.- 3-3. Eigenblades and Invariant Spaces.- 3-4. Symmetric and Skew-symmetric Transformations.- 3-5. Normal and Orthogonal Transformations.- 3-6. Canonical Forms for General Linear Transformations.- 3-7. Metric Tensors and Isometries.- 3-8. Isometries and Spinors of PseudoEuclidean Spaces.- 3-9. Linear Multivector Functions.- 3-10. Tensors.- 4 / Calculus on Vector Manifolds.- 4-1. Vector Manifolds.- 4-2. Projection, Shape and Curl.- 4-3. Intrinsic Derivatives and Lie Brackets.- 4-4. Curl and Pseudoscalar.- 4-5. Transformations of Vector Manifolds.- 4-6. Computation of Induced Transformations.- 4-7. Complex Numbers and Conformal Transformations.- 5 / Differential Geometry of Vector Manifolds.- 5-1. Curl and Curvature.- 5-2. Hypersurfaces in Euclidean Space.- 5-3. Related Geometries.- 5-4. Parallelism and Projectively Related Geometries.- 5-5. Conformally Related Geometries.- 5-6. Induced Geometries.- 6 / The Method of Mobiles.- 6-1. Frames and Coordinates.- 6-2. Mobiles and Curvature 230.- 6-3. Curves and Comoving Frames.- 6-4. The Calculus of Differential Forms.- 7 / Directed Integration Theory.- 7-1. Directed Integrals.- 7-2. Derivatives from Integrals.- 7-3. The Fundamental Theorem of Calculus.- 7-4. Antiderivatives, Analytic Functions and Complex Variables.- 7-5. Changing Integration Variables.- 7-6. Inverse and Implicit Functions.- 7-7. Winding Numbers.- 7-8. The Gauss-Bonnet Theorem.- 8 / Lie Groups and Lie Algebras.- 8-1. General Theory.- 8-2. Computation.- 8-3. Classification.- References.

ISBN: 9789027725615
ISBN-10: 9027725616
Series: Fundamental Theories of Physics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 314
Published: August 1987
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.69 x 15.6  x 1.96
Weight (kg): 0.53
Edition Type: New edition