Analysis 1 is an introductory course in real analysis designed for first-year mathematics students. It provides the foundational tools for rigorous mathematical reasoning, focusing on the real number system, sequences, limits, continuity, and differentiation. Students learn to construct precise proofs and to understand key concepts such as convergence, monotonicity, and the behavior of functions. The course emphasizes the formal definition of limits, the properties of continuous functions, and the rules of differentiation, preparing students for more advanced studies in analysis and related fields.