Books in Ordinary differential equations

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

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-dynamical 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.

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.

Comparison and Oscillation Theory of Linear Differential Equations

1st Edition
February 17, 2016
C. A. Swanson
Richard Bellman
English
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.

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.

Introductory Differential Equations

4th Edition
July 22, 2014
Martha L. Abell + 1 more
English
eBook
9 7 8 0 1 2 4 1 7 2 8 2 1

Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. The book 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. This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. It follows a traditional approach and includes ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide array of exercises ranging from straightforward to challenging. There are also new applications and extended projects made relevant to everyday life through the use of examples in a broad range of contexts. This book will be of interest to undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering.

Stochastic Differential Equations and Diffusion Processes

2nd Edition
Volume 24
June 28, 2014
N. Ikeda + 1 more
English
eBook
9 7 8 1 4 8 3 2 9 6 1 5 9

Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.

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Books in Ordinary differential equations

Difference Equations and Applications

Introductory Differential Equations

Advanced Differential Equations

A Modern Introduction to Differential Equations

Foundations of Mathematical System Dynamics

Analytical Solution Methods for Boundary Value Problems

Comparison and Oscillation Theory of Linear Differential Equations

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

Introductory Differential Equations

Stochastic Differential Equations and Diffusion Processes