Across the country, physics faculty acknowledge that solving problems using various computational methods is important, but many faculty lack the expertise and time to incorporate computational methodologies into their courses. By focusing on two core numerical algorithms (Euler method and finite difference) that are sufficient to solve a large number of problems encountered by students in traditional courses, a new, yet practical, model to integrate computation throughout the curriculum is being developed. The approach introduces these computational methods to students in their sophomore year, and then applies them comprehensively throughout the upper-division physics and astronomy curriculum with increasing levels of sophistication. Peer instruction and collaborative learning strategies are used to enhance the learning processes. New curricular materials are being developed for faculty to allow them to effectively and efficiently incorporate these computational methodologies into their courses.