Introduction to complex variables and applications

  title={Introduction to complex variables and applications},
  author={Ruel Vance Churchill},
New Method of Solving the Economic Complex Systems
A direct method used to solve the linear nonhomogeneous time-invariant difference equation with the same number for inputs and outputs is developed and the proposed theorems originally belonging to engineering to the field of economic applications are applied. Expand
The z -Transform and Analysis of LTI Systems in the Transform Domain
The DTFT may not exist for all sequences due to the convergence condition, whereas the z-transform exists for many sequences for which the DTFT does not exist. Also, the z-transform allows simpleExpand
Fourier spectral methods for numerical solving the problem of boundary control of the linear wave equation
Abstract In this paper, a Fourier spectral method is used to reduce the optimal boundary control problem for a two-dimensional wave equation to a countable number of control problems for aExpand
On the summation of divergent, truncated, and underspecified power series via asymptotic approximants
A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method onlyExpand
Transforms of Discrete-Time Signals
In this chapter, the invertible transforms used to work on discrete-time signals are discussed. Given a complex variable z, the z-transform is defined as an infinite series in the z-plane that existsExpand
Why the Last Century’s Quantum Mechanics (QM) is Irrelevant in a Duplex, Reciprocal Subspace, Reference Frame for Our Cognitive World
Nature is always richer in untapped possibilities than we think it is. We must always keep planting the new “seed corn” of fundamental research so that we might reveal new levels of nature’sExpand
Cavitation and Bubble Dynamics: Nomenclature
Cavitation and Bubble Dynamics deals with the fundamental physical processes of bubble dynamics and the phenomenon of cavitation. It is ideal for graduate students and research engineers andExpand
Low-frequency asymmetric vibrations of a tn shell with sign-changing curvature.
Most problems in Applied Mathematics involving difficulties such as nonlinear governing equations and boundary conditions, variable coefficients and complex boundary shapes preclude exact solutions.Expand
Multipole method to calculate borehole thermal resistances in a borehole heat exchanger
Ground-source heat pump systems use borehole heat exchangers to transfer heat to and from the ground. An important feature is the local thermal resistances between the heat carrier flow channels inExpand
A STM point-probe method for measuring sheet resistance of ultrathin metallic films on semiconducting silicon
Abstract We report a novel approach for distinguishing surface, bulk and space–charge layer conductivities of metalized semiconductor surfaces. The method employs current injection from the tip of aExpand