Analysis 1

This course aims to introduce students to the applications of Taylor expansions, particularly their use in simplifying complex mathematical expressions in algorithms and in estimating errors arising from numerical computations and approximation methods. It also covers the main aspects of integral calculus through the study of the Riemann integral and fundamental techniques for computing antiderivatives. Furthermore, the course provides an introduction to solving first- and second-order differential equations and their basic applications. In addition, it seeks to generalize the notions of continuity and differentiability to functions defined on subsets of ℝⁿ, thereby preparing students for the study of multivariable analysis.