This is a student-oriented text, combining throrough explanations, accurate mathematical presentation, and well-defined terms. Essays, contributed by mathematicians and written on the topics of their choosing, are included. The applications approach gives the right amount of theoretical content needed at this level. A complete revision of the chapter on numerical methods now includes new material on the Adams-Bashford Adams-Moulton multistep methods. A chapter is included on plane autonomous systems and stability which and includes a long section on applications.