Quantum Scientific Calculus, Book 1, uniquely addresses all of the rules and applications of Differential Calculus necessary for the AP Calculus AB and BC courses. The material is presented in a modular format of 90 lessons that allows great flexibility for the student and teacher. Lessons begin with the precalculus topics of the understanding functions and limits, discuss the definition of the derivative and all differentiation rules, and investigate applications of the derivative including curve sketching, optimization, and differentials. The lessons are designed to be rigorous enough for the serious student, yet user friendly enough for the independent learner. All lessons include worked examples as well as exercises with solutions.