Differential Equations and Linear Algebra

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. 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. For individuals seeking a solid, accessible introduction to differential equations and linear algebra.