Essential ordinary differential equations / Robert Magnus.
2023
QA371
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Details
Title
Essential ordinary differential equations / Robert Magnus.
Author
Magnus, Robert, author.
ISBN
9783031115318 (electronic bk.)
3031115317 (electronic bk.)
3031115309
9783031115301
3031115317 (electronic bk.)
3031115309
9783031115301
Published
Cham : Springer, [2023]
Copyright
©2023
Language
English
Description
1 online resource (xi, 283 pages) : illustrations.
Item Number
10.1007/978-3-031-11531-8 doi
Call Number
QA371
Dewey Decimal Classification
515/.35
Summary
This textbook offers an engaging account of the theory of ordinary differential equations intended for advanced undergraduate students of mathematics. Informed by the authors 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 Greens functions. The next chapters cover separable equations and other problems solvable by quadratures, series solutions of linear equations and matrix exponentials, culminating in SturmLiouville 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.
Note
Includes index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Springer undergraduate mathematics series.
Available in Other Form
ESSENTIAL ORDINARY DIFFERENTIAL EQUATIONS.
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Table of Contents
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.
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.