Course: 2020/2021

Calculus I

(15364)

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

- % 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.