Course: 2019/2020

Calculus I

(15489)

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 and the resolution of equations.

Description of contents: programme

1. Real variable functions.
1.1 The real line.
1.2 Elemmentary functions.
1.3 Limits of functions.
1.4 Continuity.
2. Differential calculus in one variable.
2.1 Derivability.
2.2 Extrema of functions.
2.3 Rolle's and Mean Value theorems.
2.4 Graphic representation.
2.5 Taylor's polynomial.
3. Sequences and series
3.1 Sequences of real numbers.
3.2 Series of real numbers.
3.3 Taylor series
4. Integration in one variable.
4.1 Integrable functions, properties of the integral and calculus of primitives.
4.2 The Fundamental Theorem of Calculus.
4.3 Improper integrals.
4.4 Applications: areas, lengths and volumes by sections.

Learning activities and methodology

The docent methodology will include:
- Master classes,
- Practical classes
- Selfevaluations.
- Partial controls.
- Tutorials.
- Final examination.

Assessment System

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

Basic Bibliography

- D. Pestana, J. M. Rodríguez, E. Romera, E, Touris, V. Álvarez y A. Portilla. Curso práctico de Cálculo y Precálculo. Ariel Ciencia. 2000
- Ron Larson y Bruce H. Edwards . Calculus I (single variable). Cengage Learning (9th edition).
- Salas/Hille/Etgen. Calculus. Una y varias varaibles (Volumen I).. Reverté, S. A.. Cuarta edición 2005

Additional Bibliography

- BURGOS, J. Cálculo infinitesimal de una variable. McGraw - Hill.
- EDWARDS, C. H., PENNEY, D. E.. Cálculo diferencial e integral. Prentice Hall.
- SPIVAK, M.. Cálculus. Reverté.
- STEWART, J.. Cálculo, conceptos y contextos. Thomson.
- THOMAS, G. B., FINNEY, R. L.. Cálculo una variable. Addison-Wesley.