Ordinary Differential Equations With Applications (Third Edition)

This book is a comprehensive textbook on Ordinary Differential Equations,Dynamical Systems,and Boundary Value Problems,with examples from physical and biological sciences and engineering. It also includes an introduction to Hamiltonian Systems.

Format: Hardback
Length: 380 pages
Publication date: 05 January 2023
Publisher: World Scientific Publishing Co Pte Ltd

This comprehensive textbook is designed to serve as a valuable resource for advanced undergraduate and first-year graduate students in mathematics, physical sciences, and engineering. Written in a straightforward and easily accessible style, it aims to provide students with a strong foundation in the theories of Ordinary Differential Equations, Dynamical Systems, and Boundary Value Problems, including regular and singular perturbations. Moreover, it serves as a valuable resource for researchers seeking to expand their knowledge in these fields.

The book is organized into nine chapters, each covering a specific topic. The first chapter introduces the fundamental concepts and theorems of Ordinary Differential Equations, including the solution of linear and non-linear equations, the theory of differential operators, and the concept of stability. The second chapter delves into Dynamical Systems, exploring the behavior of systems subjected to external forces and the principles of stability and chaos.

The third chapter focuses on Boundary Value Problems, which involve solving differential equations with boundary conditions. It covers the methods of solving boundary value problems, including the method of characteristics, the shooting method, and the Laplace transform. The fourth chapter introduces the concept of singular perturbations and discusses the stability and behavior of solutions to Ordinary Differential Equations with singular perturbations.

The fifth chapter explores the theory of Monotone Dynamical Systems, which is a branch of mathematics that deals with systems that change continuously but remain bounded. It discusses the properties of monotone systems, including the existence and uniqueness of solutions, the theory of Lyapunov functions, and the stability of monotone systems.

The sixth chapter introduces the concept of Hamiltonian Systems, which are systems of differential equations that are governed by a Hamiltonian function. It discusses the properties of Hamiltonian systems, including the conservation of energy, the stability of orbits, and the Hamilton-Jacobi equation.

The seventh chapter focuses on the applications of Ordinary Differential Equations in physical and biological sciences, including fluid dynamics, population dynamics, and the modeling of biological systems. The eighth chapter explores the applications of Dynamical Systems in engineering, including control systems, mechanical systems, and electrical systems.

The ninth chapter introduces the concept of Hamiltonian Systems in Mathematical Biology and Classical Mechanics, which is a rapidly growing field of research. It discusses the applications of Hamiltonian Systems in modeling biological systems, including the dynamics of gene expression systems, the behavior of neurons, and the evolution of populations.

Throughout the book, numerous examples and exercises are provided to illustrate the theoretical concepts and applications. These examples are drawn from physical and biological sciences, engineering, and other fields, and they help students to understand the practical implications of the theorems discussed in the text.

In addition, a chapter on Monotone Dynamical Systems is included in this third edition to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics. This chapter discusses the new developments in Ordinary Differential Equations and Dynamical Systems, including the theory of Hamiltonian Systems with applications in Mathematical Biology and Classical Mechanics.

Overall, this textbook is an essential resource for students and researchers interested in advancing their knowledge in the theories of Ordinary Differential Equations, Dynamical Systems, and Boundary Value Problems. Its comprehensive coverage, clear explanations, and numerous examples make it an invaluable tool for anyone seeking to excel in these fields.

ISBN-13: 9789811250743