Textbook in PDF format

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.
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
Epilogue