Sierpinski (<1K)Maths for (Games) Programmers
Section 5 - Multivector Calculus

Multivector Derivatives
    Multivector Functions as Tensors
          Fields     Tensors     Forms     Dyads     Multitensors     Extended Fields     Outtermorphisms   and Determinants     Eigenblades     Coordinate-based Tensor representations
          Directed Scalar Derivatives     Linearity of the Differential     Differentiating Exponentials     The Directed Chain Rule     Primary Differential     Second Primary Differential     Third Primary Differential     Secondary Differential     Lie Product
    Undirected Derivatives
          1-derivative     Ñ     Useful Ñ results     Ñ in Alternate Coordinate Systems     Monogenic Functions     Laplacian     Ñ2     Useful Ñ2 results     Multiderivative operator       Ñ     Difference between Derivatives and Differentials     Curl     ÑÙ     Partial Undirected Derivate     Secondary Undirected Derivative        ÑÞ     Simplicial Derivative     Ñ(r)     Conveyed Derivative     Ñ     Operating on and with Ñ
          The Undirected Chain Rule     The Kinematic Rules     Taylor's Formula     Contraction and Trace     Covariance     Symmetry and Skewsymmetry
    Characterising General Functions
          Connections     Directed Multivector Derivatives
    Multivector Fractals

Multivector Manifolds
    Curves and Manifolds
          Extended Mapspace     Submanifolds     Embedded Frame     Inverse Embedded Frame     Local Orientation     The Metric     M-Curve as an M-blade-valued field     Projector 1-multitensor     ¯
    Integration over an M-curve
    Fourier Transform
    Differentiation within an M-curve
          Directed Tangential Derivative     Я     Undirected Tangential 1-Derivative     Ñ
    Fundamental Theorem of Calculus
          Basic Form     Greens Functions     General Form
    Poles and Residues
          Cauchy's Theorem

Manifold Restricted Tensors
    Further differentials and derivatives
          Operator Notations        Tangential 1-differential  Ñ     Directed Coderivative      Ð()     Coderivative     Ñ     Projection Differential (1.2)-tensor     ¯Ñ     Projection Second Differential (1;3)-tensor     ¯Ñ2     Squared Projection Differential (1;3)-tensor     (¯Ñ)2     Shape (<0.2>;1)-multitensor     [ѯ]     Squape 1-multitensor     [ѯ]2     Ricci 1-tensor       ([ѯ]2¯)
    Curvature 2-tensor     [ѯ]×
          Scalar Curvature (0;1)-tensor         R = ÑÞ [ѯ]2¯     Einstein 1-tensor         (1-½ÑÞ)[ѯ]2¯

The Coordinate based approach
    Streamline Coordinates
    Lie Derivative
          Lie Bracket     Lie Drag     Lie Derivative     Covariant Frame     Covectors     Parallel transport     Linear Connection     Directed Coderivative     Geodesics
          1-Curvaturem     2-Curvature   as ortho bi-circle     Curvature Measures     Curvature Mesaures of Polyhedral 2-curves     Curvature as loop integative limit     Curvature as Coderivative Operator     Symmetries and Bianci Relations

References/Source Material

Glossary   Contents   Author
Copyright (c) Ian C G Bell 1998, 2014
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Latest Edit: 04 Oct 2014.