DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS

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.

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.

Key Features:

• The book presents many good examples explained mathematically by differential equations, making it an interesting read
• Demonstrates applications of differential equations to practical problems encountered in various familiar phenomena