I find infinitesimals more intuitive than the formal 'limits-based' approach. I'm currently studying my old degree material but using a fairly interesting book:
"Full Frontal Calculus: An Infinitesimal Approach" by Seth Braver.
I like his readable style. His poetic intro finally gave me an intuition why infinitesimals might be useful, compared to the good old reals:
"Yet, by developing a "calculus of infinitesimals" (as it was known for two centuries), mathematicians got great insight into `real` functions, breaking through the static algebraic ice shelf to reach a flowing world of motion below, changing and evolving in time."
"Full Frontal Calculus: An Infinitesimal Approach" by Seth Braver.
I like his readable style. His poetic intro finally gave me an intuition why infinitesimals might be useful, compared to the good old reals:
"Yet, by developing a "calculus of infinitesimals" (as it was known for two centuries), mathematicians got great insight into `real` functions, breaking through the static algebraic ice shelf to reach a flowing world of motion below, changing and evolving in time."