Textbook in PDF format Differential equations are completely fundamental to modern science and engineering. Differential equations have wide applications in various engineering and science disciplines. In general, modeling of the variation of a physical quantity, such as temperature, pressure, displacement, velocity, stress, strain, current, voltage, or concentration of a pollutant, with the change of time or location, or both would result in differential equations. Almost all of the known laws of physics and chemistry are actually differential equations, and differential equation models are used extensively in biology to study biochemical reactions, population dynamics, organism growth, and the spread of diseases. The most common use of differential equations in science is to model dynamical systems, i.e. systems that change in time according to some fixed rule. Differential equations arising in mechanics, physics, engineering, biological sciences, economics, and other fields of sciences may be classified into either linear or nonlinear formulated as initial or boundary value problems. The nonlinear problems are mostly difficult in obtaining a meaning full solution. For engineers, the purpose of learning the theory of differential equations is to be able to solve practical problems where differential equations are used. For engineering students, it is more important to know the applications and techniques for solving application problems than to delve into the nuances of mathematical concepts and theorems. Knowing the appropriate applications can motivate them to study the mathematical concepts and techniques. Differential Equations with Applications is concerned with the theory and the application of differential equations that examine the state of the art, identify emerging trends, and suggest future directions for developing fields. Containing original research articles as well as review articles on differential equations, and related integral equations, this book is addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools