Course: 2022/2023

Calculus I

(15489)

By the end of this content area, students will be able to have:
1. Knowledge and understanding of the mathematical principles underlying their branch of engineering.
2. The ability to apply their knowledge and understanding to identify, formulate and solve mathematical problems using established methods.
3. The ability to select and use appropriate tools and methods to solve mathematical problems.
4. The ability to combine theory and practice to solve mathematical problems.
5. The ability to understanding of mathematical methods and procedures, their area of application and their limitations.

Skills and learning outcomes

Description of contents: programme

1. Real variable functions.
1.1 The real line.
1.2 Elemmentary functions.
2. Sequences and series
3.1 Sequences of real numbers.
3.2 Series of real numbers.
3. Differential calculus in one variable.
3.1 Limits of functions.
3.2 Continuity.
3.3 Derivability.
3.4 Extrema of functions.
3.5 Rolle's and Mean Value theorems.
3.6 Graphic representation.
3.7 Taylor's polynomial.
3.8 Taylor's 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.

The course syllabus may change due academic events or other reasons.