Properties of real numbers. Real functions of one real variable. Continuity and derivability. Graphic representation. Polynomic approximation. Sequences and series of real numbers and of functions. Integration. Properties of the integral and calculus of antiderivatives. Calculation of plane areas, lengths and revolution volumes.

**MARINA DELGADO TÉLLEZ DE CEPEDA**

Department of Mathematics

Universidad Carlos III de Madrid

Area:

Mathematics

Degree:

Bachelor in Audiovisual System Engineering, Communication System Engineering and Telematics Engineering

December, 2009

21 hours of lectures + 21 hours of problem class

Total time (including hours of class): 150 hours

Elementary algebraic operations. Knowledge obtained from "bachillerato" or "módulo profesional" (highschool level).

Properties of real numbers. Real functions of one real variable. Continuity and derivability. Graphic representation. Polynomic approximation. Sequences and series of real numbers and of functions. Integration. Properties of the integral and calculus of antiderivatives. Calculation of plane areas, lengths and revolution volumes.

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, he/she will manage sequences and series of real numbers and of functions that will apply to numeric approximation of functions and the resolution of equations.

Lecture notes and presentations

Tests and exams

Problem sheets

Tests and exams

Citation: Cepeda, M. D. T. d. (2009, February 09). Calculus I. Retrieved August 05, 2020, from Web site: http://ocw.uc3m.es/matematicas/calculus-i.

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