I have got confused now. Math history seems to allow knowing all the data on how math formed, for any of a particular utility (?), and seems to allow having experiences as they were had in the history. This seems to allow having experiences on the principles of the creation of math too. And it seems to allow knowing the subject, as it really is.
And textbooks seem to give no historical data, often. They seem to give experiences in a particular order, as needed, and might eliminate problems which may have been faced before, in the history, from not having them, in the needed time. I am now knowing calculus, for knowing particle physics, quantum mechanics, etc. properly; so I seem to know the utility of math I am studying.
Reading history, seems to confirm knowing the subject and even allow knowing the recurring conformations or principles, which allow creation of math, but seems to take time.
I don't have time now; in college, they are running. I am far behind. I have stopped, since knowing zero dimensional points, irrational numbers location on the number line, zeno's paradoxes, and non-clarity in me on knowing integration/differentiation process.
I don't know the consequences of leaving historical development; if they are any, we may be able to know conformations for eliminating any of them, which would not allow attaining any of the particular intended utilities.
And I searched text books which would be self contained in all the data, and which would give all the experiences, to solve any of the problems as zeno, irrationality, etc. I have till now seen:
Courant, Richard, Differential and integral calculus.
Apostol, Tom M., Calculus. Vol. I: One variable calculus, with an introduction to linear algebra.
Lang, Serge, A first course in calculus.
being mentioned often. Which textbook would you recommend for me? Or would you recommend reading any other set of books in a particular order?