Each chapter of the book deals with mathematical modelling through one or more specified techniques. Thus there are chapters on mathematical modelling through algebra, geometry, trigonometry and calculus, through ordinary differential equations of first and second order, through systems of differential equations, through difference equations, through partial differential equations, through functional equations and integral equations, through delay-differential, differential-difference and integro-differential equations, through calculus of variations and dynamic programming, through graphs, through mathematical programming, maximum principle and maximum entropy principle. Each chapter contains mathematical models from physical, biological, social, management sciences and engineering and technology and illustrates unity in diversity of mathematical sciences. The book contains plenty of exercises in mathematical modelling and is aimed to give a panoramic view of applications of modelling in all fields of knowledge. It contains both probabilistic and deterministic models. The book presumes only the knowledge of undergraduate mathematics and can be used as a textbook at senior undergraduate or postgraduate level for a one or two-semester course for students of mathematics, statistics, physical, social and biological sciences and engineering. It can also be useful for all users of mathematics and for all mathematical modellers. Prof.

J.N. Kapur is currently Honorary Professor in School of Computer and Systems Sciences, Jawahar Lal Nehru University, Honorary Director, Mathematical Sciences Trust Society, Chief editor, Mathematical Education and President, Vigyan Parishad of India. Earlier he was Professor of Mathematics at IIT Kanpur, a vi.