Applied Pseudoanalytic Function Theory
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Beschreibung
Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods.
The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations.
It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations.
Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods.
The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations.
It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations.
First presentation in book of pseudoanalytic function theory applied to a variety of models of mathematical physics Presents new methods for studying models of mathematical physics Clearly written, at the level of an undergraduate student acquainted with complex analysis and basics of differential equations Includes supplementary material: sn.pub/extras
Autor*in
Vladislav V. Kravchenko
Themen in »Applied Pseudoanalytic Function Theory«
Dirac equation Function theory Klein-Gordon equation Riccati equation Schrödinger equation Sturm-Liouville theory analytic function elliptic equation mathematical physics ordinary differential equation pseudoanalytic function partial differential equations
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From the reviews:
“This book presents a renaissance of Bers’ and Vekua’s theory. It can be recommended to colleagues which are interested in the plane function theory.” (Michael Reissig, Zentralblatt MATH, Vol. 1182, 2010)()