02 - tensor calculus - tensor algebra

102 - tensor calculus02 - tensor calculus - tensor algebra2tensor calculustensor the word tensor was introducedin 1846 by william rowan hamilton. it wasused in its current meaning by woldemarvoigt in 1899. tensor calculus was deve-loped around 1890 by gregorio ricci-curba-stro under the title absolute differentialcalculus. in the 20th century, the subjectcame to be known as tensor analysis, andachieved broader acceptance with the intro-duction of einsteins's theory of generalrelativity around 1915. tensors are usedalso in other fields such as calculus3tensor calculustensor calculus - repetition tensor analysis vector algebranotation, euklidian vector space, scalar product, vectorproduct, scalar triple productnotation, scalar products, dyadic product, invariants, trace,determinant, inverse, spectral decomposition, sym-skewdecomposition, vol-dev decomposition, orthogonal tensorderivatives, gradient, divergence, laplace operator, integraltransformations tensor algebra4tensor calculusvector algebra .

• tensor algebra. tensor calculus 4 vector algebra - notation • summation over any indices that appear twice in a term • einstein‘s summation convention. tensor calculus 5 vector algebra - notation • permutation symbol • kronecker symbol. tensor calculus 6

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