Calculus I is the first course in the calculus sequence of the School of Sciences and serves as an introduction to the language, methods, and formal reasoning of higher mathematics. The course develops the foundations of single-variable differential calculus, starting from the structure of the real numbers and progressing through functions, limits, continuity, and differentiation, with constant emphasis on modeling phenomena involving change.
In particular, during the initial section on real numbers, I place special emphasis on understanding basic operations from a rigorous perspective. In many elementary treatments, technical details are often skipped for the sake of speed, especially when manipulating formulas or using basic operations. For this reason, the course begins with a careful discussion of fundamental concepts such as the square root function and the absolute value, ensuring that these notions are properly understood both algebraically and geometrically.
Throughout the course, intuitive ideas are always accompanied by concrete examples and geometric interpretations. This approach aims to bridge formal definitions—such as limits and derivatives—with their intuitive meaning, allowing students to develop both technical proficiency and conceptual understanding.
This collection features working notes and derivations developed throughout the semesters. Designed to complement standard textbooks, these documents focus on the rigorous construction of definitions and provide detailed walkthroughs of complex examples often omitted in class due to time constraints.
A compilation of exercise sheets and homework assignments. These problems range from computational practice to theoretical proofs, aimed at reinforcing the student's ability to formalize intuitive arguments using the $\epsilon-\delta$ language.
