Guerlebeck K., Sproessig W. Quaternionic and Clifford calculus for physicists and engineers

John Wiley & Sons Ltd., 1997, 375 p. A monograph, particularly a textbook, should have messages. Our book is intended to give three messages:
1. One variable complex analysis has a pendant in higher dimensional Euclidean space the so-called Clifford analysis.
2. Clifford and quaternionic analysis are natural approaches for the treatment of elliptic boundary value problems in higher dimensions.
3. There exists a discrete Clifford calculus, which supports a corresponding numerical analysis.
The book is addressed to mathematicians, physicists, and engineers who are interested in the analysis of partial differential equations together with their applications in mathematical physics. Our intention is to equip the reader (user) with some elementary tools for the analytical and numerical treatment of boundary value problems. Of course, we have to pay a certain price in realizing this intention. The price is a lack of generality, the restriction to special (but not too small) classes of equations and problems. Because we also explain the history of the used methods we hope to enable the reader to adapt the methods to his own problems. A corresponding part on numerical analysis is included. We have to consider that any multidimensional theory is not easy in general. We believe that Clifford analysis enables us to enter into higher dimensions in a natural way, assuming that the reader is familiar with the first steps in one variable complex function theory, basic knowledge in functional analysis, and algebra.