(Ebook) Differential Equations: A Toolbox for modeling the world by Kurt Bryan ISBN 9781638779377, 1638779376

(Ebook) Differential Equations: A Toolbox for modeling the world by Kurt Bryan ISBN 9781638779377, 1638779376

This textbook was written for a first course in ordinary differential equations for undergraduate students pursuing majors in mathematics, engineering, and science. The approach of the book is to use real-world phenomena to construct mathematical models based on differential equations in such a way that undergraduate students are motivated to learn the material and understand the usefulness of differential equations in a variety of problems.  

This book can also be useful for many non-specialist readers who may be interested in some real-world applications of differential equations. It includes explanations of the objectives and initial assumptions used in the models. The book starts with a stimulating real-world situation related to the Olympic 100-Meter Dash and presents a model that attempts to describe the position of a sprinter during the 100-meters. Examples like this help to motivate students to observe immediate applications of differential equations.

The author covers essential topics for a first course in ordinary differential equations, such as first-order linear equations, direction fields, second-order differential equations and Laplace transforms to solve differential equations.  In addition to these topics, the book includes some basic numerical methods to solve differential equations and linear and nonlinear systems of differential equations. Thus, the book covers essential aspects of the first course on differential equations plus additional material that is edifying for both students and general readers. Interestingly, the book also briefly covers deeper topics such as bifurcations, nondimensional rescaling and the matrix exponential, which serves as a rapid introduction to these areas.  The only aspect related to ordinary differential equations that this book does not include is series solutions.