> Even early calc instruction tends to be broken-- we make things complicated over various historical analytic crises, but then we take enough shortcuts in expl

> Even early calc instruction tends to be broken-- we make things complicated over various historical analytic crises, but then we take enough shortcuts in explanation that we still need to relearn half of everything when we take an actual analysis class. Take a look at Calculus Made Easy. It's non-rigorous - it uses infinitesimals without the machinery of non-standard analysis, instead of limits - but it presents the material in a clear and concise way such that just about anyone who can do basic algebra and computations can learn the material and develop an intuition for how calculus works. Once the intimidation factor is gone, they can go back and learn about epsilon-delta etc.