Retaining the same general organizational structure as its popular predecessors, this edition combines a sound and accurate exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation which have proved useful in a wide variety of applications. This updated text includes nearly 300 new problems, many of which assume the availability of computers; an expanded discussion of error control and stability; numerous new and revised problems and examples that investigate the manner in which a solution depends on one or more parameters; and greater emphasis on visualization.