| Titre : |
Essential Ordinary Differential Equations |
| Type de document : |
texte imprimé |
| Auteurs : |
Robert Magnus, Auteur |
| Mention d'édition : |
1éd. |
| Editeur : |
France: Springer Nature Switzerland AG |
| Année de publication : |
2023 |
| Collection : |
Springer Undergraduate mathematice series, ISSN 16152085 |
| Importance : |
283p. |
| Présentation : |
Couverture externe,figures |
| Format : |
24X16cm |
| ISBN/ISSN/EAN : |
978-3-031-11530-1 |
| Note générale : |
Afterword:p.279
Index:p.281 |
| Langues : |
Anglais moyen (ca.1100-1500) (enm) Langues originales : Anglais moyen (ca.1100-1500) (enm) |
| Catégories : |
2 Science
|
| Mots-clés : |
Mathematics,separation equations |
| Index. décimale : |
515 |
| Résumé : |
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. |
| Note de contenu : |
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
|
Essential Ordinary Differential Equations [texte imprimé] / Robert Magnus, Auteur . - 1éd. . - [S.l.] : France: Springer Nature Switzerland AG, 2023 . - 283p. : Couverture externe,figures ; 24X16cm. - ( Springer Undergraduate mathematice series, ISSN 16152085) . ISBN : 978-3-031-11530-1 Afterword:p.279
Index:p.281 Langues : Anglais moyen (ca.1100-1500) ( enm) Langues originales : Anglais moyen (ca.1100-1500) ( enm)
| Catégories : |
2 Science
|
| Mots-clés : |
Mathematics,separation equations |
| Index. décimale : |
515 |
| Résumé : |
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. |
| Note de contenu : |
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
|
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