Fundamentals of Ordinary Differential Equations
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Beschreibung
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.
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.
Introduces ODEs with a focus on qualitative aspects to help students develop mathematical maturity Provides an accessible approach with many examples, calculations, and proofs that are motivated and carefully introduced Contains two appendices that describe the orbits of the planets and historical notes to better illustrate these concepts
Autor*in
Uri Elias
Themen in »Fundamentals of Ordinary Differential Equations«
Ordinary differential equations ODEs First-order differential equations Existence and uniqueness theorems Linear ordinary differential equations and systems Qualitative investigation Phase plane analysis Laplace transform