Essential Ordinary Differential Equations

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Sprache: Englisch

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Beschreibung

This textbook offers an engaging account of the theory of ordinary differential equations intended for advanced undergraduate students of mathematics. Informed by the author¿s extensive teaching experience, the book presents a series of carefully selected topics that, taken together, cover an essential body of knowledge in the field. Each topic is treated rigorously and in depth.

The book begins with a thorough treatment of linear differential equations, including general boundary conditions and Green¿s functions. The next chapters cover separable equations and other problems solvable by quadratures, series solutions of linear equations and matrix exponentials, culminating in Sturm¿Liouville theory, an indispensable tool for partial differential equations and mathematical physics. The theoretical underpinnings of the material, namely, the existence and uniqueness of solutions and dependence on initial values, are treated at length. A noteworthy feature ofthis book is the inclusion of project sections, which go beyond the main text by introducing important further topics, guiding the student by alternating exercises and explanations.

Designed to serve as the basis for a course for upper undergraduate students, the prerequisites for this book are a rigorous grounding in analysis (real and complex), multivariate calculus and linear algebra. Some familiarity with metric spaces is also helpful. The numerous exercises of the text provide ample opportunities for practice, and the aforementioned projects can be used for guided study. Some exercises have hints to help make the book suitable for independent study.

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Über den Autor

In a long career as a university teacher Robert Magnus has taught most subjects in the area of analysis, including ordinary differential equations both at undergraduate and postgraduate level. He has published papers in areas allied to analysis, including non-linear partial differential equations.

Zusammenfassung

Presents carefully selected, essential topics treated in depth with mathematical rigor

Includes both linear and nonlinear theory

Contains projects for further study

Inhaltsverzeichnis

1. Linear Ordinary Differential Equations.- 2. Separation of Variables.- 3. Series Solutions of Linear Equations.- 4. Existence Theory.- 5. The Exponential of a Matrix.- 6. Continuation of Solutions.- 7. Sturm-Liouville Theory.- Afterword.

Details

Erscheinungsjahr:	2022
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xi 283 S. 1 s/w Illustr. 283 p. 1 illus.
ISBN-13:	9783031115301
ISBN-10:	3031115309
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Magnus, Robert
Auflage:	1st ed. 2023
Hersteller:	Springer International Publishing Springer International Publishing AG Springer Undergraduate Mathematics Series
Maße:	235 x 155 x 17 mm
Von/Mit:	Robert Magnus
Erscheinungsdatum:	26.11.2022
Gewicht:	0,452 kg

Artikel-ID: 122015080