Ordinary Differential Equations (Methods of Solutions, Qualitative Behavior, Existence and Uniqueness, Initial Values)

This book will introduce many physical applications of first-order ordinary differential equations, including biology, demography, economy, and finance. The theoretical framework is focused on the Cauchy problem and general solutions of homogeneous and nonhomogeneous second-order linear differential equations. The book also introduces second-order equations with applications to physics and mechanics and more advanced topics based on systems of first-order linear equations with applications to the spread of infections, cow rumen, prey, and predator modeling. The book will also contain topics on series solutions for first- and second-order linear equations, Laplace transform, and an introduction to stochastic differential equations and their applications in finance.

This book is intended for students with minimal mathematical backgrounds, It is suitable for a one semester introductory course on Ordinary Differential Equations. The topics covered have important physical applications. The author has made a special effort to make the explanations simple and descriptive, instead of formal and rigorous. It contains hundreds of examples and exercises with complete solutions to the even numbered exercises. A special feature of this book is that solutions to exercises are given with the same kind of detailed explanations as the rest of the book. The author taught differential equations classes for decades at several universities in the U.S. and also in Venezuela. The author has made a special effort to make this book cost-effective, brief and user-friendly.