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Ordinary differential equation

About: Ordinary differential equation is a(n) research topic. Over the lifetime, 33149 publication(s) have been published within this topic receiving 590467 citation(s). The topic is also known as: ODE.
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Book
01 Jan 1943-
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform

27,337 citations


Book
01 Jan 1964-
Abstract: Foreword to the Classics Edition Preface to the First Edition Preface to the Second Edition Errata I: Preliminaries II: Existence III: Differential In qualities and Uniqueness IV: Linear Differential Equations V: Dependence on Initial Conditions and Parameters VI: Total and Partial Differential Equations VII: The Poincare-Bendixson Theory VIII: Plane Stationary Points IX: Invariant Manifolds and Linearizations X: Perturbed Linear Systems XI: Linear Second Order Equations XII: Use of Implicity Function and Fixed Point Theorems XIII: Dichotomies for Solutions of Linear Equations XIV: Miscellany on Monotomy Hints for Exercises References Index.

8,982 citations


Book
01 Jan 2004-
Abstract: This handbook is the fourth volume in a series of volumes devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. It covers a variety of problems in ordinary differential equations. It provides pure mathematical and real world applications. It is written for mathematicians and scientists of many related fields.

7,736 citations


Book
01 Jan 1955-
Abstract: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable. It has been developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician.

7,066 citations



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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202240
20211,723
20201,871
20191,734
20181,656
20171,446

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Topic's top 5 most impactful authors

Dumitru Baleanu

121 papers, 3.1K citations

Fazal M. Mahomed

80 papers, 1.3K citations

Tasawar Hayat

60 papers, 2.3K citations

Ravi P. Agarwal

58 papers, 1.1K citations

Mohamed Suleiman

57 papers, 448 citations