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Books in Ordinary differential equations

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11-20 of 53 results in All results

Ordinary Differential Equations

  • 1st Edition
  • Volume 13
  • June 28, 2014
  • J. Kurzweil
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 7 6 5 - 1
The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations.The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.

Nonlinear Equations in Abstract Spaces

  • 1st Edition
  • May 27, 2014
  • V. Lakshmikantham
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 7 2 1 0 - 8
Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations.

Numerical Methods for Differential Systems

  • 1st Edition
  • May 12, 2014
  • L. Lapidus + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 6 9 8 5 - 6
Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.

Differential Forms

  • 2nd Edition
  • February 19, 2014
  • Steven H. Weintraub
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 3 9 4 4 0 3 - 0
  • eBook
    9 7 8 - 0 - 1 2 - 3 9 4 6 1 7 - 1
Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications. They both unify and simplify results in concrete settings, and allow them to be clearly and effectively generalized to more abstract settings. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems. Differential Forms, Second Edition, is a solid resource for students and professionals needing a general understanding of the mathematical theory and to be able to apply that theory into practice.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

  • 3rd Edition
  • March 12, 2012
  • Morris W. Hirsch + 2 more
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 3 8 2 0 1 0 - 5
  • eBook
    9 7 8 - 0 - 1 2 - 3 8 2 0 1 1 - 2
Hirsch, Devaney, and Smale’s classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.

Patterns and Waves

  • 1st Edition
  • September 22, 2011
  • T. Nishida + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 5 3 9 - 2
Part I of this volume surveys the developments in the analysis of nonlinear phenomena in Japan during the past decade, while Part II consists of up-to-date original papers concerning qualitative theories and their applications.Dealt with here are nonlinear problems related to general analysis, fluid dynamics, mathematical biology and computer sciences, and their underlying mathematical structures, e.g. nonlinear waves and propagations, bifurcation phenomena, chaotic phenomena, and fractals.The volume is dedicated to Professor Masaya Yamaguti in celebration of his 60th birthday.

Second Order Linear Differential Equations in Banach Spaces

  • 1st Edition
  • Volume 108
  • August 18, 2011
  • H.O. Fattorini
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 1 9 - 3
Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.