Employing a unique, reader-friendly approach to teaching differential equations, the authors present a book that encourages users to think qualitatively first and quantitatively second when approaching differential equations. Before finding the analytical solution of a differential equation, the book presents the qualitative aspects of the problem—the directional field, the bounded solutions, their range, the presence of constant solutions and so on—to help readers use linear algebra to think about the physical systems being modeled. KEY TOPICS- Topics covered include first-order differential equations, linearity and nonlinearity, linear analysis, linear transformations, linear and nonlinear systems of differential equations, forced systems, discrete dynamical systems and control theory. MARKET- For individuals seeking a solid, accessible introduction to differential equations and linear algebra.Features and Benefits Qualitative and quantitative analysis. Provides students with a “feel” for the equations that enables them to explore a common-sense line of questioning and encourages students to think about dynamical systems. Computer graphics analysis approach. Provides students with a real understanding of nonlinear differential equations. Illustrations and figures. Provides students with a clear visualization of concepts presented and has three times as many figures as competing texts. IDE software. Provides students with a CD of software that illustrates concepts presented and allows the student to experiment visually with differential equations. Qualitative analysis of nonlinear systems. Provides students with a graphics approach that enables them to gain the ability to quickly observe the effects of changing parameters and easily apply its applications in other disciplines. Discrete dynamical systems. Provides students with a current and realistic approach to the more complicated behaviors occurring in discrete iterative systems. Control theory. Enables instructors to teach one of the most important applications of differential equations. Consisent approach. Similar methods are used to solve multiple equations here by reinforcing concepts.