The theory of multivectors and multivector fields of \(K\)-th order in \(m\)-dimensional Riemann and Euclidean spaces and its applications to some multidimensional problems of mathematical physics are presented.
In Chapter 1 the algebra of multivectors in Riemann space is constructed. Different kinds of multiplication of vector, multivector, arbitrary tensor of the second rank by a multivector of \(K\)-th order are defined and their properties are studied. Chapter 2 is devoted to the foundations of multivector analysis. Integral theorems are proved and some types of multivector fields (potential, solenoidal, harmonic) are considered. In Chapter 3 the theory is applied to multivector Poisson equations, Lamé equations, multidimensional elastic theory and to the basic problem of multivector field theory, the determining of a multivector field by its gradient and cogradient.