Preface

Ordinary differential equations are powerful tools for modeling and analyzing complex phenomena in various fields. Understanding ODEs is essential for making accurate predictions, optimizing systems, and solving real-world problems. ODEs are vital tools in study involving climate change, population dynamics, economic growth, chemical reaction, resource management, epidemiological growth of diseases and pandemic and drug administration.

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

This book comprises nine chapters and it is on ‘Vector valued ordinary differential equations and applications’. The Chapters are written bearing in mind beginners in the field of study who have little or no background on the course. 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.

The first chapter contains preliminaries like set theory, topological concepts and the formulation of vector differential equations. The second chapter and the third chapter are on Linear differential equations in the linear space , basic concepts related to topological structures are discussed such structures are Normed and Banach spaces as applicable to solutions of ordinary differential equations. The proof of existence and uniqueness of solution for initial value problems (IVP), the ‘power house’ of course finds its shape from fixed points. Peano’s existence theorem and Picard Lindelof theorem are exploited in no small measure. The fourth chapter is on solutions to matrix initial value problems.

The fifth chapter is about canonical transformation, a kind of transformation from scalar equations to vector equations. This chapter ends with the treatment of exponential matrices and estimation theory. The sixth is on Stability theory, Stability is a kind of graduation from continuous dependence on initial data localized to some finite interval of E  (,) to more global generalized concepts. The seventh chapters examine the linear periodic systems with the Floquent rule extensively utilized. Also treated in this chapter are stability of linear perturbed systems and applications to neural firing models, avian influenza, population models. The ninth chapter is on numerical solutions to ODEs and applications to some models respectively

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.