The Non-Algebraic Elementary Functions: a Rigorous Approach.

From the author's Preface: "The principle objective of this text is training the student for a rigorous calculus course. It is my conviction that a course in elementary functions or advanced trigonometry is the natural place to begin building the foundation for future rigorous mathematical studies. It is certainly the natural place to introduce the idea of functions and limiting processes which the student will need not only in calculus but in much of his future mathematical work.