This book is written for students and researchers who are fond of mathematics and the natural sciences. It consists of two parts. Part I presents the theory of analysis in which the mathematical theory is described not as an accomplished palace, but as a building under construction. It uncovers how a theory has been or is being constructed. In Part II, the theory of differential equations is applied to interesting practical problems, such as pursuit-line and tractrix, attack on an object from an airplane, an insect crawling along a stretching rubber rod, the SIR model of a virus infection, string vibration, circular membrane vibration, as well as the wind ripple, sand dune and wave phenomena on a highway. Furthermore, the problems of a one-dimensional lattice vibration, the keyboard percussion vibration and the eigenvalue problems in quantum mechanics, such as the Aharonov–Bohm effect, are also investigated in detail. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction to the Theory of Analysis Contents: Theories: Introduction to the Theory of Analysis Differential Equations Differential Operators Applications: Ordinary Differential Equations Partial Differential Equations Problems Involving Bessel Functions Potential Problems in Quantum Mechanics Readership: Undergraduate students, postgraduate students and researchers interested in the theory and applications of differential equations in mathematics and the natural sciences.