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Course: 2020/2021

Calculus I

(15364)

Study: Bachelor in Telecommunication Technologies Engineering (252)

Coordinating teacher: HERNANDO OTER, PEDRO JOSE

Department assigned to the subject: Department of Mathematics

Type: Basic Core

ECTS Credits: 6.0 ECTS

Course: 1º

Semester: 1º

Branch of knowledge: Engineering and Architecture

Competences and skills that will be acquired and learning results. Further information on this link

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. (PO: a)

Description of contents: programme

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.

Learning activities and methodology

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

Assessment System

We follow a continuous-assessment system plus a final exam:

 - The continuous-assessment part consists in two exams with a 40% weight on the final mark (20% each). The exams will take place, approximately a week after the necessary lessons have been taught and it will be held in regular class hours, according to the current regulations.

 - The final exam (contributing with weight 60% to the final mark) is compulsory, and will be held at the end of the semester. (PO: a.)

% end-of-term-examination 60
% of continuous assessment (assigments, laboratory, practicals...) 40

Basic Bibliography

Gilbert Strang. Calculus. Wellesley-Cambridge Press. 1991
J. Stewart. Calculus. Thomson Brooks/Cole. 2009
JUAN de BURGOS ROMAN. Funciones de una variable. Límites, continuidad y Derivadas. 80 Problemas Útiles. García Maroto Editores, Madrid 2006.
JUAN de BURGOS ROMAN. Cálculo Integral (una y varias variables). 70 Problemas Útiles. García Maroto Editores, Madrid 2006.
JUAN de BURGOS ROMAN. Cálculo Infinitesimal: Definiciones, Teoremas y Resultados. Maroto Editores, Madrid 2006.

Additional Bibliography

Juan Diego Álvarez Román y Manuel Carretero Cerrajero. Cálculo: Un enfoque práctico. Copy Red. S.A, Getafe . 2009
R. LARSON, R. HOSTETLER y B. EDWARDS. Cálculo I. Reverté, 1994.
S.L. SALAS Y E. HILLE. Calculus (primer tomo). Reverté, 1994.
T.M. APOSTOL. Calculus (2 tomos). Iberoamericana.

The course syllabus and the academic weekly planning may change due academic events or other reasons.