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This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them. The book is organized around this approach with important topics, such as existence, uniqueness, qualitative behaviour, and stability, appearing in early chapters and explicit solution methods covered later. Proofs are included in an approachable manner, which are first motivated by describing the main ideas in a general sense before being written out in detail. A clear and accessible writing style is used, containing numerous examples and calculations throughout the text. Two appendices offer readers further material to explore, with the first using the orbits of the planets as an illustrative example and the second providing insightful historical notes. After reading this book, students will have a strong foundation for a course in PDEs or mathematical modeling.
Fundamentals of Ordinary Differential Equations is suitable for an undergraduate course for students who have taken basic calculus and linear algebra courses, and who are able to read and write basic proofs. Because of its detailed approach, it is also conducive to self-study.
Table des matières
What is an ordinary differential equation?.- First-order differential equations.- Existence and uniqueness theorems.- Linear equations of higher order.- Systems of differential equations.- The qualitative theory and the phase plane.- Solution of differential equations by power series.- The Laplace transform.- Appendix: The orbits of the planets.- Appendix: Historical notes.
A propos de l'auteur
Uri Elias is a Professor Emeritus at the Technion - Israel Institute of Technology in Haifa. His research interest is Ordinary Differential Equations. Much of his research has centered on the study of oscillation and qualitative theory of O.D.E., some of which is published in the book "Oscillation Theory of Two-Term Differential Equations", Springer, Mathematics and Its Applications, Vol. 396. Uri Elias's aim in teaching is to introduce O.D.E.s and their behavior while keeping everything as clear and precise as possible.
Résumé
This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them. The book is organized around this approach with important topics, such as existence, uniqueness, qualitative behaviour, and stability, appearing in early chapters and explicit solution methods covered later. Proofs are included in an approachable manner, which are first motivated by describing the main ideas in a general sense before being written out in detail. A clear and accessible writing style is used, containing numerous examples and calculations throughout the text. Two appendices offer readers further material to explore, with the first using the orbits of the planets as an illustrative example and the second providing insightful historical notes. After reading this book, students will have a strong foundation for a course in PDEs or mathematical modeling.
Fundamentals of Ordinary Differential Equations is suitable for an undergraduate course for students who have taken basic calculus and linear algebra courses, and who are able to read and write basic proofs. Because of its detailed approach, it is also conducive to self-study.
