Introduction

The difference between advanced calculus and calculus is that all the theorems are proved completely and the role of plane geometry is minimized. Instead, the notion of completeness is of preeminent importance. Formal manipulations are of no significance at all unless they aid in showing something significant. Routine skills involving elementary functions and integration techniques are supposed to be mastered and have no place in advanced calculus which deals with the fundamental issues related to existence and meaning. This is a subject which places calculus as part of mathematics and involves proofs and definitions, not algorithms and busy work.

An orderly development of the elementary functions is included but it is assumed the reader is familiar enough with these functions to use them in problems which illustrate some of the ideas presented.

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