This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This text, Part I, contains the first five chapters of the course and two appendices. Chapters included are: (1) Polynomial Functions; (2) The Derivative of a Polynomial Function; (3) Circular Functions; (4) Derivatives of Circular Functions; and (5) Exponential and Related Functions. The appendices are: (1) Functions and Their Representations; and (2) Polynomials. (RH)