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Ellipsoidal Harmonics by George Dassios

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Appendix BElements of dyadic analysis

The dyadic representation is very useful when: (i) we deal with more than one base; (ii) we use curvilinear coordinates where differential operators need to act on the components as well as on the base elements; (iii) we represent solutions of equations in a way that separates the variables from the parameters of the problem; (iv) we perform successive algebraic operations in a systematic way; and (v) we present complicated expressions in a compact and meaningful form. The theory of dyadics was introduced and developed by J. Willard Gibbs and can be found in his celebrated book Vector Analysis, written by E. B. Wilson [159]. Nevertheless, the most complete introduction to polyadics is contained in the monumental ...

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