This is the Table of Contents and Chapter 1 of SIMIODE's digital textbook, Differential Equations: A Toolbox for Modeling the World, by Kurt Bryan, ISBN 978-1-63877-937-7.
Authored by the distinguished teacher and writer, Dr. Kurt Bryan, Rose-Hulman Institute of Technology, Terre Haute IN USA, this text takes a modeling first and throughout approach to motivate the study and learning of differential equations in the spirit of SIMIODE, while linking to many SIMIODE Modeling Scenarios and other original activities.
SIMIODE offers this digital online textbook, Differential Equations: A Toolbox for Modeling the World (ISBN 978-1-63877-937-7) to purchase for $39USD. Your purchase helps to support SIMIODE's mission and community of practice.
Purchasers of this textbook will be invited to engage in a SIMIODE Textbook - Teacher Group or a SIMIODE Textbook - Student Group where all the resources appropriate to the respective interests of the group will be provided: solutions, hints, project ideas, data, computer code, forums, collaborative project space, etc.
Differential Equations: A Toolbox for Modeling the World puts applications and modeling front and center in an introduction to ordinary differential equations. In taking this approach we do not skimp on or skip over the mathematics, but use applications to motivate both subject and technique. The mathematics presented is interwoven with modeling to drive both the mathematics and understanding of the application under study and to make the case that differential equations provide a powerful, indispensable toolbox for describing the world.
Dr. Glenn Ledder, University of Nebraska, Lincoln NE USA, says in his forthcoming review in The UMAP Journal, “This book is the only one this reviewer is aware of that presents differential equations in a modeling context rather than merely adding a bit of modeling to the standard presentation. If you want to study the mathematics of differential equations in a modeling context, you are in the right place.”
We also present some unconventional, but important topics not usually offered in introductory texts: dimensional analysis, parameter estimation, a brief introduction to control theory via Laplace transforms, nondimensionalizing and scaling of differential equations, and a more thorough treatment of electrical circuits. The text includes numerous exercises, including inline “Reading Exercises,” as well as a section of more extensive modeling projects at the end of each chapter, many based on published SIMIODE projects, and many new activities. Several projects include data sets for experimentation and model validation.
Again, purchase this textbook, support SIMIODE, and enjoy the read.
This work was supported in part by the National Science Foundation through NSF:DUE-IUSE Grant # 1940532.