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Differential Equations With Maxima

Author: Drumi D. Bainov
Publisher: CRC Press
ISBN: 1439867585
Size: 43.29 MB
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Differential equations with "maxima"—differential equations that contain the maximum of the unknown function over a previous interval—adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various technical systems on which our ever-advancing, high-tech world depends. Understanding and manipulating the theoretical results and investigations of differential equations with maxima opens the door to enormous possibilities for applications to real-world processes and phenomena. Presenting the qualitative theory and approximate methods, Differential Equations with Maxima begins with an introduction to the mathematical apparatus of integral inequalities involving maxima of unknown functions. The authors solve various types of linear and nonlinear integral inequalities, study both cases of single and double integral inequalities, and illustrate several direct applications of solved inequalities. They also present general properties of solutions as well as existence results for initial value and boundary value problems. Later chapters offer stability results with definitions of different types of stability with sufficient conditions and include investigations based on appropriate modifications of the Razumikhin technique by applying Lyapunov functions. The text covers the main concepts of oscillation theory and methods applied to initial and boundary value problems, combining the method of lower and upper solutions with appropriate monotone methods and introducing algorithms for constructing sequences of successive approximations. The book concludes with a systematic development of the averaging method for differential equations with maxima as applied to first-order and neutral equations. It also explores different schemes for averaging, partial averaging, partially additive averaging, and partially multiplicative averaging. A solid overview of the field, this book guides theoretical and applied researchers in mathematics toward further investigations and applications of these equations for a more accurate study of real-world problems.

Mathematical Modeling Of Discontinuous Processes

Author: Andrey Antonov
Publisher: Scientific Research Publishing, Inc. USA
ISBN: 1618964402
Size: 66.66 MB
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In this monograph as a mathematical apparatus are used and investigated several classes of differential equations. The most significant feature of these differential equations is the presence of impulsive effects. The main goals and the results achieved in the monograph are related to the use of this class of equation for an adequate description of the dynamics of several types of processes that are subject to discrete external interventions and change the speed of development. In all proposed models the following requirements have met: 1) Presented and studied mathematical models in the book are extensions of existing known in the literature models of real objects and related processes. 2) Generalizations of the studied models are related to the admission of external impulsive effects, which lead to “jump-like” change the quantity characteristics of the described object as well as the rate of its modification. 3) Sufficient conditions which guarantee certain qualities of the dynamics of the quantities of the modeled objects are found. 4) Studies of the qualities of the modification of the modeled objects are possible to be successful by differential equations with variable structure and impulsive effects. 5) The considerations relating to the existence of the studied properties of dynamic objects cannot be realized without introducing new concepts and proving of appropriate theorems. The main objectives can be conditionally divided into several parts: 1) New classes of differential equations with variable structure and impulses are introduced and studied; 2) Specific properties of the above-mentioned class of differential equations are introduced and studied. The present monograph consists of an introduction and seven chapters. Each chapter contains several sections.

Hadamard Type Fractional Differential Equations Inclusions And Inequalities

Author: Bashir Ahmad
Publisher: Springer
ISBN: 3319521411
Size: 47.48 MB
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This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.

Calculus In Vector Spaces Second Edition Revised Expanded

Author: Lawrence Corwin
Publisher: CRC Press
ISBN: 9780824792794
Size: 13.74 MB
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Calculus in Vector Spaces addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This second edition introduces, among other topics, the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space, allowing for Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting. Mathematical analysts, algebraists, engineers, physicists, and students taking advanced calculus and linear algebra courses should find this book useful.

Methoden Der Mathematischen Physik

Author: Richard Courant
Publisher: Springer-Verlag
ISBN: 366236445X
Size: 59.92 MB
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Stabilit Tstheorie

Author: P.C. Parks
Publisher: Springer
ISBN: 9783540110019
Size: 34.14 MB
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Das vorliegende Buch entstand aus der ausgearbeiteten Mitschrift der Vorlesung "Stabilitätstheorie", die Herr Prof. Parks im Winter semester 1979/80 als Gastprofessor an der Ruhr-Universität in Bochum hielt. Diese Vorlesung wandte sich an Studenten der Regelungstechnik, die über Grundkenntnisse der mathematischen Beschreibung dynamischer Vorgänge mittels Differentialgleichungen verfügten. Obwohl die Sta bilität dynamischer Systeme vom technischen Standpunkt aus darge stellt wird, ist das Buch auch für den Leser von Interesse, der mit dynamischen Prozessen im nichttechnischen Bereich, z. B. der Biokyber netik, der Meteorologie, usw. zu tun hat. Das Buch erfordert - abge sehen von dem Verständnis zur Beschreibung dynamischer Vorgäng- keine besonderen Vorkenntnisse vom Leser und ist als Einführung in das Gebiet gut geeignet. Andererseits wird ein Uberblick über sehr viele Methoden der Stabilitätsprüfung gegeben, so daß es für den jenigen, der sich schnell über eine Methode informieren will, durch aus als "Nachschlagewerk" verwendbar ist. Besonderer Wert wurde da rauf gelegt, nicht nur die Anwendung der einzelnen Methoden, sondern auch ihre Ableitung und ihre Zusammenhänge dazustellen. Insofern ist das Buch eine sinnvolle Ergänzung der bisherigen Lehrbuchliteratur auf dem Gebiet der Stabilität dynamischer Systeme. Ich wünsche dem vorliegenden Buch, daß es vor allem auch in der Praxis Interesse findet und Anlaß zur weiteren Anwendung der vor geschlagenen Verfahren wird. Professor Dr. -Ing. H. Unbehauen Lehrstuhl für Elektrische Steuerung und Regelung Ruhr-Universität Bochum Bochum, im Sommer 1981 Inhaltsverzeichnis 0. Einführung •. . . . . . •. . . . . . . . . . . . . . . ••. . ••. •. ••. . •. . . •. . . . . . 1. Stabilitätstheorie linearer Systeme . . . . . . . •. •. . . . . . . . . . . .