China
Africa
Explore chapters and articles related to this topic
Electric Field Calculations
Published in Robert M. Del Vecchio, Bertrand Poulin, Pierre T. Feghali, Dilipkumar M. Shah, Rajendra Ahuja, Transformer Design Principles, 2017
Robert M. Del Vecchio, Bertrand Poulin, Pierre T. Feghali, Dilipkumar M. Shah, Rajendra Ahuja
In the theory of functions of a complex variable, analytic functions play a special role. Analytic functions are functions that are continuous and differentiable in some region of the complex plane. Functions which satisfy Equation 11.46 are called harmonic functions. In addition, analytic mappings from one complex plane to another have properties that allow a solution of Equation 11.46 in a relatively simple geometry in one complex plane to be transformed to a solution of this equation in a more complicated geometry in another complex plane. We briefly describe some of the important properties of these functions that are needed in the present application. See [Chu60] for further details.
Conformal Transformation
Published in Matthew N. O. Sadiku, Sudarshan R. Nelatury, Analytical Techniques in Electromagnetics, 2015
Matthew N. O. Sadiku, Sudarshan R. Nelatury
To begin with, we introduce the fundamental notions of complex variables and the concept of analytic function and discuss several basic mappings [1–5]. The real and imaginary parts of an analytic function obey Cauchy–Riemann equations and individually satisfy the two-dimensional Laplace equation. An immediate consequence of this is the possibility of defining a complex potential function with real and imaginary parts denoting the flux function and the associated equipotential function.
Power Series Solutions II: Generalizations and Theory
Published in Kenneth B. Howell, Ordinary Differential Equations, 2019
Analytic continuation is any procedure that “continues” an analytic function defined on one region so that it becomes defined on a larger region. Perhaps it would be better to call it “analytic extension” because what we are really doing is extending the domain of our original function by creating an analytic function with a larger domain that equals the original function over the original domain.
Mathematical modeling of electromagnetic radiations incident on a symmetric slit with Leontovich conditions in an-isotropic medium
Published in Waves in Random and Complex Media, 2023
Analytic Continuation:Letandbe analytic functions on domainsand, respectively, and suppose that the intersectionis not empty and thatonThenis called an analytic continuation oftoand vice versa. Moreover, if it exists, the analytic continuation oftois unique.