I think for a very elementary calculus course, one would do better teaching only physics. In particular, I would remove the complication of integration methods, except for the more elementary ones. I would give more emphasis to the meaning of differential equations. I would focus in constructing models and fiddling around with them, and giving the appropriate definitions along the way.
For the next level of calculus, I would use Spivak's text that is definitely more advanced, but gives a flavor of real math together with a huge set of wonderful exercises.