Differential Equations: A Dynamical Systems Approach to Theory and Practice
dec. de 2021 · American Mathematical Society
Libro electrónico
536
Páxinas
Acerca deste libro electrónico
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time—pure and applied alike—ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present t...
Descubrir máis
Valora este libro electrónico
Dános a túa opinión.
Información de lectura
Smartphones e tabletas
Instala a aplicación Google Play Libros para Android e iPad/iPhone. Sincronízase automaticamente coa túa conta e permíteche ler contido en liña ou sen conexión desde calquera lugar.
Portátiles e ordenadores de escritorio
Podes escoitar os audiolibros comprados en Google Play a través do navegador web do ordenador.
Lectores de libros electrónicos e outros dispositivos
Para ler contido en dispositivos de tinta electrónica, como os lectores de libros electrónicos Kobo, é necesario descargar un ficheiro e transferilo ao dispositivo. Sigue as instrucións detalladas do Centro de axuda para transferir ficheiros a lectores electrónicos admitidos.
