We describe two college-level introductory courses in physics, with calculus prerequisites, that are entirely computer-based. These courses have been developed by the Education Program for Gifted Youth (EPGY) at Stanford, a research project that provides year-round, accelerated instruction in mathematics and physics to gifted or advanced middle- and high-school students via computer-based courseware. Students in EPGY run multimedia courseware at home or in school on personal computers using the MS-Windows operating system. Our software, unlike traditional applications of computers in education, is intended to be the primary means of instruction and not merely a supplement to a regular class. It is precisely in those settings in which a regular class cannot be offered, either because of an insufficient number of students or the absence of a qualified instructor, that our software is intended to be used. Because we are concerned with college-level physics courses, which presuppose calculus, the issue of teacher qualification is a significant one. We have used our course model over the last four years to teach advanced-placement (AP) calculus and physics courses to gifted middle- and advanced high-school students. The remainder of the article focuses on the EPGY course software in the context of the AP physics courses.