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Essential ordinary differential equa...

Magnus, Robert.

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Essential ordinary differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Essential ordinary differential equations/ by Robert Magnus.
Author:	Magnus, Robert.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xi, 283 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Differential equations. -
Online resource:	https://doi.org/10.1007/978-3-031-11531-8
ISBN:	9783031115318

Essential ordinary differential equations
Magnus, Robert.

Essential ordinary differential equations[electronic resource] /by Robert Magnus. - Cham :Springer International Publishing :2023. - xi, 283 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,2197-4144. - Springer undergraduate mathematics series..

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.

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 of this 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.

ISBN: 9783031115318

Standard No.: 10.1007/978-3-031-11531-8doiSubjects--Topical Terms:

517952
Differential equations.

LC Class. No.: QA371

Dewey Class. No.: 515.35

Essential ordinary differential equations
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490 1 $a Springer undergraduate mathematics series, $x 2197-4144
505 0 $a 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.
520 $a 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 of this 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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