Advanced Calculus: Problems And Applications To Science And Engineering

In 1963, I taught from that text to a class of exceptionally brilliant students at Princeton University. I believe that course was successful and influential for those students. As the text has no illustrative material, I developed a set of notes of " classical " advanced calculus which we used as a supplement to the text. This was the beginning of the present textbook of advanced calculus.
I began to feel that indeed algebra, geometry, and topology are cornerstones of modern mathematical analysis, but so is "classical" advanced calculus. I decided that we needed a bridge between freshman calculus and modern analysis which leaned heavily upon the techniques of algebra and the concepts of geometry. This text is an attempt at such a bridge. In 1967, I taught from a preliminary edition to a class of physics-motivated juniors, and in 1968 I taught from what is essentially the present text to a class of sophomores. These two classes have had a profound influence on the development of the text and I am deeply indebted to them for assistance in matters of style and pedagogy.