By most books I assume you mean pretty college US text books. I have no experience with them, are they really that bad ? My previous college calculus was far f

By most books I assume you mean pretty college US text books. I have no experience with them, are they really that bad ? My previous college calculus was far from the rigour of Rudin but also far from a cookbook flavour. Unless by 'cookbook' you mean the chain rule and differentials of standard forms. It's not that hard to teach this stuff at least it's no harder than, say, geometry. I found trigonometry far more difficult. We were first taught limits then came differentiation of polynomials using infitesimals.Chain rule was introduced. Then we ventured into differentiation of other functions. Integration was first introduced much like riemann integrals then came integration as an inverse of differentiation.