On Systems of Ordinary, Non-Linear Differential Equations Involving Periodic Given Functions With a Small Period (Classic Reprint) - Softcover
Inhaltsangabe
Explore how periodic inputs shape nonlinear differential systems with a rigorous, paper‑and‑pencil approach that ties theory to concrete estimates. This book develops an averaging framework for ordinary differential equations where the right‑hand side depends on a small period and shows how time averages lead to smoother, easier‑to‑analyze problems.
The author builds the theory step by step, starting from Lipschitz conditions and integral formulations, then proving key lemmas and a central existence theorem. Throughout, two themes recur: how to craft practical bounds and how to relate a complex, time‑varying system to a simpler averaged version that preserves essential behavior. An included example illustrates the method on a moving‑particle model, highlighting how estimates translate into concrete statements about displacement and velocity.
- How periodic forcing and small periods affect nonlinear systems of ODEs
- How to construct and bound time‑averaged functions and their Lipschitz properties
- How integral equations relate to differential equations and how existence/uniqueness is established
- Practical techniques for estimating key quantities such as p(t) and the time horizon T
Ideal for readers with a background in differential equations who want a solid, calculation‑driven treatment of averaging methods in nonlinear, time‑dependent problems, including worked examples and clear estimation strategies.
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On Systems of Ordinary (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book explores the behavior of periodic systems of ordinary differential equations with small periods, offering numerical estimates that have applications in applied mathematics. The author utilizes the concept of time averaging to approximate solutions over finite time intervals. By examining specific functions, the book establishes conditions under which solutions can be well-approximated by solutions to systems with time-averaged functions. The estimates provided enable practical use in mathematical physics and other fields that involve such equations, aiding in the analysis and prediction of system behavior. The book's insights deepen our understanding of the dynamics of periodic systems with small periods and their relevance in various scientific disciplines. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332928194_0
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On Systems of Ordinary, NonLinear Differential Equations Involving Periodic Given Functions With a Small Period Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781332928194
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On Systems of Ordinary, NonLinear Differential Equations Involving Periodic Given Functions With a Small Period Classic Reprint
Anbieter: PBShop.store UK, Fairford, GLOS, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781332928194
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