A new two-semester sequence is being developed that includes differential equations and linear algebra and that is based on the philosophy and spirit of the first year calculus course developed under the Five Colleges Calculus in Context Project. Students gain a better grasp of the concepts of calculus when they are presented in the context of real and substantial applications that require a combination of techniques and that involve open-ended problems that often do not have clean, simple solutions. Writing and the use of computers are an integral part of this approach.