An intuitive approach to calculus

Extract

“A derivative is a linear transformation which approximates a function near to a point.” I heard this definition for the first time in 1964, in a lecture at Oxford on the calculus of several variables (the lecturer was D.A. Edwards). The words came as a revelation, and from then on I had a new conception of differential calculus. At school, I thought that I knew about calculus because I could write out proofs of differentiation ‘from first principles’. I enjoyed going through the hoops and proving that δy/δ tends to a limit, but somehow the idea of differentiation never became ‘part of me’.