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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.
List of contents
First-Order Differential Equations.- Linear Systems.- Autonomous Systems.- Perturbation Methods.- The Self-Adjoint Second-Order Differential Equation.- Linear Differential Equations of Order n.- BVPs for Nonlinear Second-Order DEs.- Existence and Uniqueness Theorems.
Summary
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.
Additional text
From the reviews of the second edition:
“A very good book on Differential Equations. It is the kind of book I would use in the classroom as well as recommend to a student for independent study. I can see it used as textbook for a course in Differential Equations … or in a one semester course for math majors. … instructors would enjoy teaching from this book, and that students would be able to study from it … at a good pace. And they would learn a lot about differential equations.” (Florin Catrina, The Mathematical Association of America, November, 2010)
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From the reviews of the second edition:
"A very good book on Differential Equations. It is the kind of book I would use in the classroom as well as recommend to a student for independent study. I can see it used as textbook for a course in Differential Equations ... or in a one semester course for math majors. ... instructors would enjoy teaching from this book, and that students would be able to study from it ... at a good pace. And they would learn a lot about differential equations." (Florin Catrina, The Mathematical Association of America, November, 2010)
