The theory of differential equations: classical and qualitative

For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written 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 well-prepared 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. - Provides 81 new problems in the exercises in addition to the problems from the first edition - Elegant and carefully written, with many examples and exercisesthroughout the book - Any needed concepts from linear algebra are introduced with examples as INDICE: Preface.- 1 First-Order Differential Equations.- 2 Linear Systems.- 3 Autonomous Systems.- 4 Perturbation Methods.- 5 The Self-Adjoint Second-Order Differential Equation.- 6 Linear Differential Equations of Order n.- 7 BVPs for Nonlinear Second-Order DEs.- 8 Existence and Uniqueness Theorems.- Solutions to Selected Problems.- Bibliography.- Index

• ISBN: 978-1-4419-5782-5
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 424
• Fecha Publicación: 01/07/2010
• Nº Volúmenes: 1
• Idioma: Inglés