Emphasis on linear equations. Linear and nonlinear equations (first order and higher order) are treated in separate chapters. Mathematical modeling. Most students studying differential equations are preparing for careers in the physical or life sciences. In developing models, this text guides the student carefully through the underlying physical principles leading to the relevant mathematics. Critical thinking. Emphasis on the importance of common sense, intuition, and “back-of-the-envelope” checks to help the student ask: “Does my answer make sense?” Interpretation of results. Many of the examples and exercises ask the student to anticipate and interpret the physical content of the solution. Reference in later courses. Provides students in science and engineering with a useful reference for their later coursework. Interactive Differential Equations. A special version of this visualization software is now available on the Web. It is mapped specifically to the organization of this text.