Applied Pseudoanalytic Function Theory

This book covers recent developments in pseudoanalytic function theory including applications and multidimensional generalizations. Written at an undergraduate level, it is the first book of the theory applied to many models of mathematical physics.

Pseudoanalytic Function Theory and Second-order Elliptic Equations. - Definitions and Results from Bers Theory. - Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions. - Formal Powers. - Cauchy s Integral Formula. - Complex Riccati Equation. - Applications to Sturm-Liouville Theory. - A Representation for Solutions of the Sturm-Liouville Equation. - Spectral Problems and Darboux Transformation. - Applications to Real First-order Systems. - Beltrami Fields. - Static Maxwell System in Axially Symmetric Inhomogeneous Media. - Hyperbolic Pseudoanalytic Functions. - Hyperbolic Numbers and Analytic Functions. - Hyperbolic Pseudoanalytic Functions. - Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation. - Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications. - The Dirac Equation. - Complex Second-order Elliptic Equations and Bicomplex Pseudoanalytic Functions. - Multidimensional Second-order Equations.