A conceptual introduction to Differential Calculus of algebraic and transcendental functions of one variable; focus on logical reasoning and fundamental notions; first introduction into a rigorous mathematical theory with applications. Course covers: real numbers, set operations, supremum, infimum, limits, continuity, Intermediate Value Theorem, derivative, differentiability, related rates, Fermat's, Extreme Value, Rolle's and Mean Value Theorems, curve sketching, optimization, and antiderivatives.