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.

CB1: Students have demonstrated possession and understanding of knowledge in an area of study that builds on the foundation of general secondary education, and is usually at a level that, while relying on advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study CG3: Knowledge of basic and technological subject areas which enable acquisition of new methods and technologies, as well as endowing the technical engineer with the versatility necessary to adapt to any new situation. RA1: Knowledge and understanding of the general fundamentals of engineering, scientific and mathematical principles, as well as those of their branch or specialty, including some knowledge at the forefront of their field.

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).