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The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity. The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus.

Clifford algebras. --- Quaternions. --- Algebra, Universal --- Algebraic fields --- Curves --- Surfaces --- Numbers, Complex --- Vector analysis --- Geometric algebras --- Algebras, Linear --- Algebra. --- Group theory. --- Topological Groups. --- Mathematical physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Associative Rings and Algebras. --- Group Theory and Generalizations. --- Topological Groups, Lie Groups. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Groups, Topological --- Continuous groups --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Mathematics --- Mathematical analysis --- Gravitation. --- Associative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Physics. --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebraic rings --- Ring theory --- Rings (Algebra) --- Properties