Differential Equations And Their Applications: Analysis From A Physicist's Viewpoint

This book is written for students and researchers who are fond of mathematics and the natural sciences, presenting the theory of analysis and the theory of differential equations applied to practical problems. It also investigates problems of a one-dimensional lattice vibration, keyboard percussion vibration, and the eigenvalue problems in quantum mechanics.

Format: Hardback
Length: 396 pages
Publication date: 26 May 2022
Publisher: World Scientific Publishing Co Pte Ltd

This book is a captivating exploration of mathematics and the natural sciences, designed specifically for students and researchers with a deep passion for these fields. It comprises two distinct parts, each offering a unique perspective on the subject matter.

Part I delves into the realm of analysis, presenting the mathematical theory as a dynamic and evolving construction. It unveils the intricate processes through which theories are built, shedding light on the construction process itself. Through this lens, readers gain a deeper understanding of the foundations upon which mathematical concepts and theories are constructed.

Part II takes the theory of differential equations and applies it to a wide range of practical problems. These problems encompass diverse scenarios, from the pursuit-line and tractrix to the attack on an object from an airplane, the crawling behavior of an insect along a stretching rubber rod, the SIR model of a virus infection, the vibration of strings, circular membrane vibrations, and even the phenomena of wind ripples, sand dunes, and wave phenomena on a highway. The book goes beyond theoretical discussions and provides detailed insights into the mathematical models and solutions that govern these real-world phenomena.

Furthermore, the book delves into the realm of one-dimensional lattice vibration, keyboard percussion vibration, and eigenvalue problems in quantum mechanics. It explores in depth the Aharonov-Bohm effect, a fundamental phenomenon in quantum physics, and other related topics. By examining these complex problems, readers gain a deeper appreciation of the mathematical principles that underpin the natural world.

In conclusion, this book is a treasure trove of knowledge and insights, catering to students and researchers who seek to expand their understanding of mathematics and the natural sciences. Whether you are a beginner or an advanced student, this book will provide you with a solid foundation and inspire you to explore the endless possibilities of these fields.

ISBN-13: 9789811247453