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This book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems. Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering. One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned. The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.

Differential equations. --- Numerical analysis. --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- Algorithms. --- Numerical Analysis. --- Differential Equations. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Equacions diferencials --- Anàlisi numèrica

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A complete new edition on ferroelectrics, Landolt-Börnstein volume III/36, is required by the growing number of publications and increasing amount of valuable data after the publication of volume III/16 (1981) and its supplement III/28 (1990). As the range of the compiled data is very extensive, volume III/36 is divided into three subvolumes titled III/36A Oxides, III/36B Inorganic substances other than oxides, III/36C Organic crystals, liquid crystals and polymers. Subvolume III/36C on organic crystals, liquid crystals and polymers is presented herewith. Volume III/36 contains revised, updated and extended information on ferroelectrics, antiferroelectrics and closely related substances. All reliable data on both pure compounds and solid solutions are critically evaluated and included. Besides of the dielectric and ferroelectric behavior, a number of other properties relevant to the characterization of the substances are presented in tables and figures.

Ferroelectric crystals. --- Liquid crystals.

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FERROELECTRIC MATERIALS --- FERROELECTRIC MATERIALS