This four-term sequence covers all the material of the 420/430/510/520 courses, with additional applications and explorations, and in greater depth. Working within contexts whenever possible, key concepts are developed with applications in mind. Students learn to read the language of differential equations, and to appreciate that the two principal divisions of calculus - differential (rate problems) and integral (accumulation problems) - are unified by the Fundamental Theorem of Calculus. Students enrolled in 431 or higher in the spring will be prepared for the AB Advanced Placement examination; students in 521 will be prepared for the BC examination. In preparation for these examinations, MAT431 and MAT521 classes in the spring term may meet during the reserve formats prior to the examination and fewer times per week after.