The theory of differential equations : classical and qualitative
 Author/Creator
 Kelley, Walter G.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 New York : Springer, c2010.
 Physical description
 xi, 423 p. : ill. ; 24 cm.
 Series
 Universitext.
Access
Contributors
 Contributor
 Peterson, Allan C.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 415417) and index.
 Contents

 Preface. Chapter 1 FirstOrder Differential Equations. 1.1 Basic Results. 1.2 FirstOrder Linear Equations. 1.3 Autonomous Equations. 1.4 Generalized Logistic Equation. 1.5 Bifurcation. 1.6 Exercises. Chapter 2 Linear Systems. 2.1 Introduction. 2.2 The Vector Equation x' = A(t)x. 2.3 The Matrix Exponential Function. 2.4 Induced Matrix Norm. 2.5 Floquet Theory. 2.6 Exercises. Chapter 3 Autonomous Systems. 3.1 Introduction. 3.2 Phase Plane Diagrams. 3.3 Phase Plane Diagrams for Linear Systems. 3.4 Stability of Nonlinear Systems. 3.5 Linearization of Nonlinear Systems. 3.6 Existence and Nonexistence of Periodic Solutions. 3.7 ThreeDimensional Systems. 3.8 Differential Equations and Mathematica. 3.9 Exercises. Chapter 4 Perturbation Methods. 4.1 Introduction. 4.2 Periodic Solutions. 4.3 Singular Perturbations. 4.4 Exercises. Chapter 5 The SelfAdjoint SecondOrder Differential Equation. 5.1 Basic Definitions. 5.2 An Interesting Example. 5.3 Cauchy Function and Variation of Constants Formula. 5.4 SturmLiouville Problems. 5.5 Zeros of Solutions and Disconjugacy. 5.6 Factorizations and Recessive and Dominant Solutions. 5.7 The Riccati Equation. 5.8 Calculus of Variations. 5.9 Green's Functions. 5.10 Exercises. Chapter 6 Linear Differential Equations of Order n. 6.1 Basic Results. 6.2 Variation of Constants Formula. 6.3 Green's Functions. 6.4 Factorizations and Principal Solutions. 6.5 Adjoint Equation. 6.6 Exercises. Chapter 7 BVPs for Nonlinear SecondOrder DEs. 7.1 Contraction Mapping Theorem (CMT). 7.2 Application of the CMT to a Forced Equation. 7.3 Applications of the CMT to BVPs. 7.4 Lower and Upper Solutions. 7.5 Nagumo Condition. 7.6 Exercises. Chapter 8 Existence and Uniqueness Theorems. 8.1 Basic Results. 8.2 Lipschitz Condition and PicardLindelof Theorem. 8.3 Equicontinuity and the AscoliArzela Theorem. 8.4 CauchyPeano Theorem. 8.5 Extendability of Solutions. 8.6 Basic ConvergenceTheorem. 8.7 Continuity of Solutions with Respect to ICs. 8.8 Kneser's Theorem. 8.9 Differentiating Solutions with Respect to ICs. 8.10 Maximum and Minimum Solutions. 8.11 Exercises. Solutions to Selected Problems. Bibliography. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefullywritten textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as perturbation methods and differential equations and Mathematica. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0. It also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many more other enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for wellprepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.
(source: Nielsen Book Data)
Subjects
 Subject
 Differential equations.
Bibliographic information
 Publication date
 2010
 Responsibility
 Walter G. Kelley, Allan C. Peterson.
 Series
 Universitext
 ISBN
 9781441957825
 1441957820
 Publisher Number
 12728800