Essential Ordinary Differential Equations - Robert Magnus

Essential Ordinary Differential Equations

(Autor)

Buch | Softcover
XI, 283 Seiten
2022 | 1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-11530-1 (ISBN)
37,44 inkl. MwSt
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.fsfsfsscs

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.

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.

Erscheinungsdatum
Reihe/Serie Springer Undergraduate Mathematics Series
Zusatzinfo XI, 283 p. 1 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 424 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte Boundary value problem • Continuation of solutions • Eigenfunction expansion • exponential of a matrix • Green's Function • Initial Value Problem • Newton's equation • One-parameter group • Ordinary differential equations • Picard existence theorem • Regular singular point • series solution of ODE • Stability Theory • Sturm-Liouville theory • Wronskian
ISBN-10 3-031-11530-9 / 3031115309
ISBN-13 978-3-031-11530-1 / 9783031115301
Zustand Neuware
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