A Modern Introduction to Dynamical Systems
Seiten
2018
Oxford University Press (Verlag)
978-0-19-874327-9 (ISBN)
Oxford University Press (Verlag)
978-0-19-874327-9 (ISBN)
A senior-level, proof-based undergraduate text in the modern theory of dynamical systems that is abstract enough to satisfy the needs of a pure mathematics audience, yet application heavy and accessible enough to merit good use as an introductory text for non-math majors.
This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising what may be called the modern theory of dynamics.
Prerequisite knowledge is restricted to calculus, linear algebra and basic differential equations, and all higher-level analysis, geometry and algebra is introduced as needed within the text. Following this text from start to finish will provide the careful reader with the tools, vocabulary and conceptual foundation necessary to continue in further self-study and begin to explore current areas of active research in dynamical systems.
This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising what may be called the modern theory of dynamics.
Prerequisite knowledge is restricted to calculus, linear algebra and basic differential equations, and all higher-level analysis, geometry and algebra is introduced as needed within the text. Following this text from start to finish will provide the careful reader with the tools, vocabulary and conceptual foundation necessary to continue in further self-study and begin to explore current areas of active research in dynamical systems.
Richard J. Brown is a Teaching Professor and the Director of Undergraduate Studies in the Mathematics Department at Johns Hopkins University. His mathematical research involves using dynamical systems to study the topological and geometrical properties of surfaces. He is also active in studying and enhancing the effectiveness of undergraduate university education in mathematics and STEM and how students and educators navigate the difficult transition between secondary school mathematics and university mathematics.
1: What is a Dynamical System?
2: Simple Dynamics
3: The Objects of Dynamics
4: Flows and Maps of Euclidean Space
5: Recurrence
6: Phase Volume Preservation
7: Complicated Orbit Structure
8: Dynamical Invariants
| Erscheinungsdatum | 21.06.2018 |
|---|---|
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 157 x 234 mm |
| Gewicht | 664 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-19-874327-0 / 0198743270 |
| ISBN-13 | 978-0-19-874327-9 / 9780198743279 |
| Zustand | Neuware |
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