Primarily intended for the undergraduate students of mathematics, physics and engineering, this text gives in-depth coverage of differential equations and the methods for solving them.
The book begins with the definitions, the physical and geometric origins of differential equations, and the methods for solving the first order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher order differential equations and their applications to telecommunications, civil engineering, cardiology and detection of diabetes, as also the methods of solving simultaneous differential equations and their applications. Besides, the book provides a detailed discussion on Laplace transforms and their applications, partial differential equations and their applications to vibration of stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications.
The book, which is a happy fusion of theory and application, would also be useful to postgraduate students.
NEW TO THIS EDITION
• New sections on:
(a) Equations reducible to linear partial differential equations
(b) General method for solving the second order non-linear partial differential equations (Monge’s Method)
(c) Lagrange’s equations of motion
• Number of solved examples in Chapters 5, 7, 8, 9 and 10.
About the Author
ZAFAR AHSAN, Ph.D., is a Professor at the Department of Mathematics, Aligarh Muslim University, Aligarh. He is the Editor of Palestine J. of Mathematics and J. of Interpolation and Approximation in Scientific Computing and Member of Editorial Boards of Global J. of Advanced Research on Classical and Modern Geometries, International e-J. of Numerical Analysis and Related Topics, Taif J. of Maths. and Stats, Islamic University of Gaza J. of Natural and Engineering Studies, J. of Tensor Society, Bull. and J. of Calcutta Mathematical Society. Professor Ahsan has been a Visiting Associate of Inter University Centre for Astronomy and Astrophysics (IUCAA), Pune (July 1996–June 2005) and a UGC Visiting Professor of Sardar Patel University, Vallabh Vidyanagar (April 2004–May 2005). He is also life member of Indian Association for General Relativity and Gravitation, Calcutta Mathematical Society, Indian Society of Industrial and Applied Mathematics, Indian Mathematical Society and Tensor Society of India and a founder member of International Electronic Engineering Mathematical Society (Egypt). Professor Zafar Ahsan has so far published 96 research papers in national and international journals of repute and has authored four books. His current research interest, apart from General Relativity and Gravitation, is on Qur’an and Modern Cosmology.
Table of Contents:
Preface • Preface to the Second Edition Preface to the First Edition 1. Basic Concepts 2. Differential Equations of First Order and First Degree 3. Equations of the First Order but not of the First Degree 4. Applications of First Order Differential Equations 5. Higher Order Linear Differential Equations 6. Applications of Higher-order Differential Equations 7. Systems of Linear Differential Equations and Their Applications 8. Laplace Transforms and Their Applications to Differential Equations 9. Partial Differential Equations and Their Applications 10. Calculus of Variations and Its Applications Bibliography • Answers to Exercises • Index
