Book Calculus of One and Many Variables by Kenneth Kuttler pdf
By Kenneth Kuttler
This book is a discussion of calculus of functions of real variables. It is written to be a first course in Calculus and to be used in the first three semesters of calculus.
However, it would also work as an advanced calculus book for those who have had the typical undergraduate calculus course. I am assuming the reader has had college algebra and trigonometry although most of what is needed is reviewed. Calculus has become a conglomeration of standard techniques, most of which can be done better with a computer algebra system, along with contrived applications, tied together with specious and/or incomplete arguments and appeals to authority.
Those aspects of the subject which are mathematically significant are marginalized, thus ignoring what was learned early in the nineteenth century. In general, existence theorems are neglected, which results in incomplete explanations of many of the most important theorems like mean value theorem, fundamental theorem of calculus etc