Ordinary Differential Equations with Applications, 3/e (Hardcover)

Written in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras. A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.

以直接且易於理解的風格撰寫，本書適合數學、物理科學和工程學的高年級本科生或一年級研究生使用。其目的是為學生提供在常微分方程、動力系統和邊界值問題的理論方面建立堅實基礎，包括常規和奇異微擾。同時，本書也是研究人員的寶貴資源。本書豐富地提供了物理學、生物學和工程學的許多實例，以說明文中定理的應用。讀者將會接觸到非線性分析中的一些重要定理，例如布勞爾不動點定理和代數的基本定理。一章專門介紹了單調動力系統，以應對常微分方程和動力系統領域的新發展。在第三版中，增加了對哈密頓系統的介紹，以增強並完善對常微分方程在數學生物學和古典力學中的應用的涵蓋範圍。