This is the first course in a three-course sequence (COS-MATH-171, -172, -173). This course includes a study of functions, continuity, and differentiability. The study of functions includes the exponential, logarithmic, and trigonometric functions. Limits of functions are used to study continuity and differentiability. The study of the derivative includes the definition, basic rules, and implicit differentiation. Applications of the derivative include optimization and related-rates problems.