MAT012, MAT021, and MAT022 — USM

Term Professor (sole instructor) at Universidad Técnica Federico Santa María. Full responsibility for the three courses below: lectures, problem sessions, assessment design, exam writing and grading, office hours, and final grade assignment.

MAT021 — Mathematics I

A theoretical and practical foundational course integrating algebra, trigonometry, and analytic geometry to introduce the language of mathematics, together with the basic concepts and techniques of differential calculus for real-valued functions of one real variable.

Topics: elementary algebra and trigonometry; analytic geometry of the plane; functions, limits, and continuity; the derivative and its applications (optimization, related rates, curve sketching); Taylor approximation.

MAT022 — Mathematics II

A theoretical and practical foundational course covering the fundamental concepts of integral calculus, series, matrix and vector algebra, and basic notions of finite-dimensional spaces, with applications to the mathematical modeling of real-world phenomena.

Topics: the definite and indefinite integral; techniques of integration; applications of integration; sequences and series, convergence tests, power series; matrix algebra and systems of linear equations; vectors in $\mathbb{R}^n$ and basic notions of finite-dimensional vector spaces.

MAT012 — Mathematics III

A theoretical and practical foundational course that delivers the fundamental concepts of integral calculus and linear algebra, with applications modeled on real-world problems across diverse disciplines.

Topics: integral calculus in one and several variables, with applications; linear algebra (vector spaces, linear maps, eigenvalues and eigenvectors); selected applications to modeling in science and engineering.