Long ago I found an introductory calculus book which started (after introducing functions) with Lipschitz continuity right away instead of the usual fundamental definitions and theorems.
I think it might have been a book for physics/science students, but I'm not sure.
I also think it was intended for beginners who haven't had any higher mathematics courses, as it introduced a lot of basic definitions and methods in a very clear and explicit way.
In any case, I wanted to ask the community if anyone remembers a book like that.
It's possible that the book was not just calculus, but some kind of general mathematics textbook. I really don't remember. But as long as it actually introduces Lipschitz right away after talking about functions, it's probably the book I'm looking for.
Yuriy S,
There have been a couple calculus textbooks that approach the topic of differentiable functions not using the notion of a limit but requiring that the tangent to such functions satisfy a second-order Lipschitz condition in an open interval around the point at which the derivative is being evaluated (i.e. the tangent line lies between two parabolas which are, themselves, tangent to the graph of the curve at that point)
The ones that immediately come to my mind are:
"Applied Calculus: Math 215" by Karl Heinz Dovermann
"Practical Analysis in One Variable" by Donald Estep
"Applied Mathematics - Body and Soul" by K. Eriksson, D. Estep, C. Johnson