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Books in Ordinary differential equations

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    • Difference Equations and Applications

      • 1st Edition
      • October 24, 2024
      • Youssef N. Raffoul
      • English
      • Paperback
        9 7 8 0 4 4 3 3 1 4 9 2 6
      • eBook
        9 7 8 0 4 4 3 3 1 4 9 3 3
      Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters.Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential.

    • Introductory Differential Equations

      • 6th Edition
      • December 21, 2023
      • Martha L. Abell + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 3 1 6 0 5 8 5
      • eBook
        9 7 8 0 4 4 3 1 6 0 5 9 2
      **2025 Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner**Introductory Differential Equations, Sixth Edition provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. The book's accessible explanations and many robust sample problems are appropriate for a first semester course in introductory ordinary differential equations (including Laplace transforms), for a second course in Fourier series and boundary value problems, and for students with no background on the subject.

    • Advanced Differential Equations

      • 1st Edition
      • April 13, 2022
      • Youssef N. Raffoul
      • English
      • Paperback
        9 7 8 0 3 2 3 9 9 2 8 0 0
      • eBook
        9 7 8 0 3 2 3 9 9 2 8 1 7
      Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations. Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations.

    • A Modern Introduction to Differential Equations

      • 3rd Edition
      • January 17, 2020
      • Henry J. Ricardo
      • English
      • Hardback
        9 7 8 0 1 2 8 2 3 4 1 7 4
      • eBook
        9 7 8 0 1 2 8 1 8 2 1 8 5
      A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical and numerical aspects of first-order equations, including slope fields and phase lines. The comprehensive resource then covers methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients, systems of linear differential equations, the Laplace transform and its applications to the solution of differential equations and systems of differential equations, and systems of nonlinear equations. Throughout the text, valuable pedagogical features support learning and teaching. Each chapter concludes with a summary of important concepts, and figures and tables are provided to help students visualize or summarize concepts. The book also includes examples and updated exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering.

    • Foundations of Mathematical System Dynamics

      • 1st Edition
      • Volume 2
      • May 25, 2017
      • George J. Klir
      • English
      • eBook
        9 7 8 1 4 8 3 2 8 6 9 7 6
      This book is a foundational study of causality as conceived in the mathematical sciences. It is shown that modern mathematical dynamics involves a formulation of the fundamental concept of causality, and an exhaustive classification of causal systems. Among them are the 'self-steering' and 'self-regulating' systems, which together form the class of purposive systems, on whose specific properties the book then focuses. These properties are the mathematical-dynamic... foundations of the behavioural and social sciences. This is the definitive book on causality and purposive processes by the originator of the mathematical concept of self-steering.

    • Comparison and Oscillation Theory of Linear Differential Equations

      • 1st Edition
      • June 3, 2016
      • C. A. Swanson
      • Richard Bellman
      • English
      • Paperback
        9 7 8 1 4 8 3 2 5 3 2 7 5
      • eBook
        9 7 8 1 4 8 3 2 6 6 6 7 1
      Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.

    • Analytical Solution Methods for Boundary Value Problems

      • 1st Edition
      • July 15, 2016
      • A.S. Yakimov
      • English
      • Hardback
        9 7 8 0 1 2 8 0 4 2 8 9 2
      • eBook
        9 7 8 0 1 2 8 0 4 3 6 3 9
      Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods.

    • Boundary Value Problems for Systems of Differential, Difference and Fractional Equations

      • 1st Edition
      • October 1, 2015
      • Johnny Henderson + 1 more
      • English
      • Paperback
        9 7 8 0 1 2 8 0 3 6 5 2 5
      • eBook
        9 7 8 0 1 2 8 0 3 6 7 9 2
      Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.

    • Numerical Methods for Differential Systems

      • 1st Edition
      • May 12, 2014
      • L. Lapidus + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 2 3 0 9
      • Hardback
        9 7 8 0 1 2 4 3 6 6 4 0 4
      • 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.

    • Ordinary Differential Equations

      • 1st Edition
      • Volume 13
      • June 28, 2014
      • J. Kurzweil
      • English
      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.