Preface

Ordinary differential equations as a branch of Mathematics has grown from a tiny mustard seed to a giant tree over the centuries. Its outgrowth could be said to have originated from simple problems of finding solutions to equations involving rates of change of the dependent variable with respect to the independent variable x or time t. For example, finding the rate at which a balloon can be inflated or deflated.

Today, human interests and logistics are diverse and go beyond this datum level. It is above a mere study of fluxion theory of Isaac Newton that could be said to be the foundation stone of differential equations.

This textbook is an encyclopedia of techniques for finding solutions to differential equations. It was developed when lecturing students and researching at the Abubakar Tafawa Balewa University, Bauchi; Kaduna State University, Kaduna, Nigerian; Nile University, Baze university, University of Abuja all in Abuja and the Plateau State University Bokkos , all in Nigeria.

This book comprises seven chapters and it is on ‘scalar differential equations’. The chapters are designed so that beginners in the field of study who have little or no background on the course can easily understand the book. This requirement is met by deployment of lucid and self-instructional language and utilization of scintillating examples throughout the book as well as illustration using Maple modeling and simulation software. Maple and MapleSim software are reconnoitered for finding symbolic solutions to problems in ODEs and simulation of engineering systems. Maple examples on how to find the analytic solutions to the ODEs problems, and plotting and animation of solution paths in 2D and 3D forms are presented.

Furthermore, among pages of ‘freshman’ Chapters are the treatment of variable separable, exact equations, the method of undetermined coefficients and variation of constant parameters method. The celebrated Green’s function technique as applicable to the boundary value problems (BVP) has also been presented with several examples from physical, biological and engineering problems. Chapter six introduces an algebraic structure, the vector space, concept of linear transformation and the differential operator ‘D method’; this method is instrumental to finding particular integrals to the differential equations. Chapter seven is on solutions of differential equations by power series.

Every part of the chapters in this textbook contains preambles without assuming students’ familiarity with some basic mathematical concepts. Hence it will prove to be a valuable and supplementary textbook for other courses in Mathematics and Engineering.