Differential Equations & Linear Algebra

For Differential Equation and Linear Algebra courses at a sophomore level.Using a unique, student-friendly approach to teaching differential equations, this text encourages students to think both quantitatively and qualitatively when approaching differential equations. Before finding the analytical solution of a differential equation, the text 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 students use linear algebra to think about the physical systems being modeled. In addition, this text features a fluid integration of linear algebra therefore emphasizing the inter-relatedness of differential equations and linear algebra.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.