Written for beginning students, this well organized introduction promotes a solid understanding of differential equations with a flexible presentation. With less emphasis on formal calculation than other texts, all the basic methods are covered—linear, separable, and exact equations—as well as higher order cases, linear equations with constant and variable coefficients, Laplace transform methods, and nonlinear systems. The text's systems focus induces an intuitive understanding of the concept of a solution of an initial value problem in order to resolve potential confusion about what is being approximated when a numerical method is used.