5 YouTube tutorials on Clifford’s geometric algebra


By E. Hitzer. At University of Nagoya, Japan. 20 Jan. 2012. Recorded by K. Tachibana, Kogakuin University, Tokyo. The presentation was part of the Monthly meeting (January 2012) of the Research Meeting on Particle Filters, Japan. It was organized by Prof. N. Ikoma of the Kyushu Institute of Technology and Prof. K. Tachibana of Kogakuin University, Tokyo.

Howto: Click on the Tutorial 1 – 5 links below.

Tutorial 1: Historical development, Clifford algebra of Euclidean plane R^2.

Tutorial 2: Clifford algebra of Euclidean space R^3, quaternions, biquaternions, versors, and spinors.

Tutorial 3: Clifford algebra of Euclidean space R^3, multiplication table, subalgebras, grade structure, duality, contractions, outer product, cross product, scalar product, norm.

Tutorial 4: Clifford algebra of Euclidean space R^3 and spacetime. Details: blade subspaces, outer and inner product null space representations, blade space subalgebras, projection, rejection, join (union), meet (intersection), involutions (reversion, main involution, Clifford conjugation). Spacetime: Spacetime algebra, Lorentz group, Lie algebra of Lorentz group, Unification of Maxwell equations, Dirac-Hestenes equation for the electron.

Tutorial 5: Conformal geometric algebra (CGA), Clifford analysis, geometric calculus. CGA: conformal points, conformal planes, linearization of translations with translation operators (translators), motion operators, Lie algebra of conformal transformations, conformal object subspaces: points, point pairs, lines, planes, circles, spheres, intersections. Clifford Analysis: multivector functions, vector differential, vector derivative, examples, rules of multivector differential calculus, multivector integral calculus, fundamental theorem of multivector calculus, path independence, Green’s, Stokes’, and Gauss’ divergence theorems, monogenic functions, Cauchy’s integral theorem in n dimensions.

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