Course: 2022/2023

Calculus I

(15364)

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.

Skills and learning outcomes

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

Assessment System

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

Basic Bibliography

- Gilbert Strang. Calculus. Wellesley-Cambridge Press. 1991
- HERNANDO, P. J.. Clases de Cálculo I para Ingeniería. Versión 2.6, PDF. 2021
- J. Stewart. Calculus. Thomson Brooks/Cole. 2009
- JUAN de BURGOS ROMAN. Cálculo Integral (una y varias variables). 70 Problemas Útiles. García 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 may change due academic events or other reasons.