The course has both an educational goal, introducing reasoning and mathematical symbolism, and calculus training. We propose the conceptual and methodological tools to understand the basic scientific language, providing the fundamentals of mathematical analysis (in one variable) and linear algebra (in two and three dimensions), oriented towards the understanding of geometric and mathematical physics models. The topics of differential and integral calculus in one variable and linear algebra are presented from both a geometric and analytical point of view and a modeling description is provided. The course aims to enable the student to understand basic mathematical concepts and use them autonomously to formulate or critically read problems and check their applications.