About the Book

Publication Date: August, 2025

This Mathematics textbook is part of the De Anza College Zero Textbook Cost (ZTC) Pathways initiative, supporting both students and instructors with free, adaptable Open Educational Resources (OER).

This book offers an accessible and thorough introduction to differential equations, focusing on both the theory and applications of first-order and higher-order differential equations, power series solutions, Laplace transforms, and systems of differential equations.

Through detailed explanations, real-world examples, and interactive elements, students learn how differential equations are used to model physical systems, population dynamics, electrical circuits, mechanical vibrations, and more. Key analytical techniques—such as separation of variables, integrating factors, exact equations, undetermined coefficients, variation of parameters, and the eigenvalue method—are presented alongside numerical methods and qualitative tools like slope fields, phase portraits, and autonomous systems.

Topics include the classification and solution of first-order differential equations using various methods, applications such as exponential growth and decay, Newton’s law of cooling, mixing problems, and pursuit curves, as well as the study of second-order and higher-order linear differential equations with constant coefficients. Students will explore nonhomogeneous equations and their applications in physical systems like spring-mass-damper models and forced oscillations. The book also introduces power series methods for solving differential equations near ordinary and singular points, including the Frobenius method, and provides a comprehensive treatment of the Laplace transform and its use in solving initial value problems. Finally, the text covers systems of differential equations, matrix methods, and the eigenvalue method for solving linear systems.

This book builds upon the foundation established in Introductory Differential Equations by Jiří Lebl and Elementary Differential Equations with Boundary Value Problems by William F. Trench. We also acknowledge Lake Tahoe Community College’s derivative of Lebl’s textbook, which served as an important starting point for our own work. In creating this resource, we have aimed to uphold the principles of open education while enhancing accessibility for a diverse range of learners. With its blend of open access, practical applications, and rich multimedia support, this textbook reflects De Anza College’s commitment to student equity, innovation, and leadership in OER.

In addition to the core text, we provide ancillary materials to enhance teaching and learning.