<p>Cal Tech's Math 1a uses Apostol's Calculus as a textbook. It could be described as a "real analysis" course. At other universities, physicists and engineers who came in with a 5 in AP Calculus BC would probably start with computationally-oriented multivariable calculus and linear algebra courses. I wonder if Cal Tech physics and engineering majors think Math 1a served them or well or if the mathematical rigor was not necessary for them.</p>
<p>You’re not missing out timing-wise compared to other schools. At Caltech, the first year’s courses cover basic rigorous set theory all the way through multivariate calculus. After the first term of rigor in Ma1a, you have the choice between an ‘analytical’ or ‘practical’ track for the rest of the freshman year. In the practical track you cover the same computationally-oriented linear algebra and multivariate calculus as you would at other schools, with the added rigorous background from the first class. It’s not just about the mathematical rigor, but about being precise and thinking critically, skills that all scientists should have (This is why we use Apostol for an introductory class)</p>
<p>Thanks for your reply. I know that when I started with electricity and magnetism in college, having only Calculus BC as preparation, it was difficult to learn the physics and the math (div, grad, and especially curl) at the same time.</p>