Overview
- Presents carefully selected, essential topics treated in depth with mathematical rigor
- Includes both linear and nonlinear theory
- Contains projects for further study
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (7 chapters)
Keywords
- Ordinary Differential Equations
- initial value problem
- boundary value problem
- Sturm-Liouville theory
- Green's function
- Newton's equation
- Picard existence theorem
- one-parameter group
- Wronskian
- series solution of ODE
- regular singular point
- exponential of a matrix
- Eigenfunction expansion
- Continuation of solutions
- stability theory
About this book
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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Authors and Affiliations
About the author
Bibliographic Information
Book Title: Essential Ordinary Differential Equations
Authors: Robert Magnus
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-031-11531-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Softcover ISBN: 978-3-031-11530-1Published: 26 November 2022
eBook ISBN: 978-3-031-11531-8Published: 24 November 2022
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XI, 283
Number of Illustrations: 1 b/w illustrations
Topics: Analysis