The student will be able to formulate, solve and understand mathematically the problems arising in engineering. To do so it is necessary, in this first course of Calculus, to be acquainted with the real functions of one variable, their properties of continuity, derivability, integrability and their graphic representation. The student will understand the concepts of derivative and integral and their practical applications. Also, it will manage sequences and series of real numbers and of functions that will apply to numeric approximation of functions.

S3_FB10: Ability to solve mathematical problems arising in engineering. Aptitude for applied knowledge in: linear algebra, geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives; numerical methods; numerical algorithms; statistics and optimization.

1) Real numbers. 2) Sequences and series of real numbers 3) Limits of Functions. Continuity. Differentiation. 4) Taylor Expansions. Local Approximations. Graphical representation. 5) Sequences and series of functions. 6) Riemann Integral. Fundamental Theorem of Calculus. Integration techniques. Geometrical Applications of Integration.

Theory (2.5 credits). Problem sessions working individually and in groups (2.5 credits).