differential equations with maxima

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Differential Equations With Maxima

Author : Drumi D. Bainov
ISBN : 9781439867587
Genre : Mathematics
File Size : 90. 72 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.

Hadamard Type Fractional Differential Equations Inclusions And Inequalities

Author : Bashir Ahmad
ISBN : 9783319521411
Genre : Mathematics
File Size : 26. 28 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.

Differential Equations The Second International Colloquium

Author : Bainov Drumi D
ISBN : 9789814554510
Genre :
File Size : 57. 9 MB
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Advanced Differential Calculus

Author : A.K. Sharma
ISBN : 8171418627
Genre :
File Size : 29. 18 MB
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Contents: Change of Independent Variables, Maxima and Minima (Of Functions of a Single Independent Variable), Maxima and Minima (Of Functions of Two Independent Variable), Maxima and Minima (Of Function of Several Independent Variable), Envelopes and Evolutes, Jacobians, Singular Points, Curve Tracing.

Multivariable Calculus Linear Algebra And Differential Equations

Author : Stanley I. Grossman
ISBN : 9781483218038
Genre : Mathematics
File Size : 69. 93 MB
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Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.

Mathematical Modeling And Simulation

Author : Kai Velten
ISBN : 9783527627615
Genre : Science
File Size : 77. 34 MB
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This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

Proceedings Of The Third International Colloquium On Differential Equations

Author : Drumi D. Bainov
ISBN : 9067641537
Genre : Science
File Size : 34. 44 MB
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The Third International Colloquium on Differential Equations was organized by UNESCO and the Plovdiv Technical University, with the help of many international mathematical organizations, and was held in Plovdiv, Bulgaria, 18--22 August 1992. This proceedings volume contains selected invited talks which deal with the following topics: -- impulsive differential equations -- nonlinear differential equations -- differential equations with maxima -- applications of differential equations

Invited Lectures Delivered At The Sixth International Colloquium On Differential Equations August 18 23 1995 Plovdiv Bulgaria

Author : Dimitŭr Baĭnov
ISBN : CORNELL:31924079652362
Genre : Mathematics
File Size : 45. 49 MB
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Numerical Methods For Partial Differential Equations

Author : William F. Ames
ISBN : 9781483262420
Genre : Mathematics
File Size : 82. 72 MB
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Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.

Annals Of Differential Equations

Author :
ISBN : UOM:39015060909762
Genre : Differential equations
File Size : 53. 23 MB
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