Course: 2019/2020

Calculus II

(13491)

Students are expected to have completed

Calculus I
Linear Algebra

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

By the end of this content area, students will be able to have:
1. Knowledge and understanding of the mathematical principles of differential and integral Calculus of several variables underlying their branch of engineering.
2. The ability to apply their knowledge and understanding to identify, formulate and solve problems related to differential and integral Calculus using established methods.
3. The ability to select and use appropriate tools and methods to solve problems of differential and integral Calculus .
4. The ability to combine theory and practice to solve problems of differential and integral Calculus.
5. The ability to understanding of mathematical methods of differential and integral Calculus and procedures, their area of ¿¿application and their limitations.
Evaluation of RAS
The first result from the student learning is evaluated through the implementation of approximated calculations, including error estimations, as obtained from the solution of optimization problems related to those found in the Electrical Power Engineering profession. These problems at the beginning are textually formulated (without the use of the mathematical notation). In a second step the Differential and Integral Calculus will be used to solve them.
The 2th, 3th, 4th and 5th results from the student learning are evaluated in a systematic way through different partial and final exams because these learning results constitute essential parts in the formation of the mathematical way of thinking required to work as an Electrical Power Engineer.

Description of contents: programme

1. Differential calculus on several variables:
1.1 Functions of several variables. Limits and continuity.
1.2 Derivatives. Differenciability.
1.3 Vectorial functions and differential operators.
1.4 Chain rule and directional derivatives.
2. Local study of functions of several variables.
2.1 Derivatives of higher order.
2.2 Extrema of functions of several variables.
2.3 Conditioned extrema.
3. Integration on Rn:
3.1 Multiple integral.
3.2 Changes of variable on multiple integrals.
3.3 Applications.
4. Line and surface integrals:
4.1 Line integrals and conservative fields.
4.2 Surface integrals.
4.3 Green, Stokes and Gauss theorems.

Learning activities and methodology

The docent methodology will include:
- Master classes, where the knowledge that the students must acquire will be presented. To make easier the development of the class, the students will have written notes and also will have the basic texts of reference that will facilitate their subsequent work.
- Resolution of exercises by the student that will serve as self-evaluation and to acquire the necessary skills.
- Problem classes, in which proposed problems are discussed and developed.
- Partial controls.
- Final exam.
- Tutorials.

Assessment System

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

Basic Bibliography

- MARSDEN, TROMBA. CALCULO VECTORIAL. ADDISON WESLEY.
- SALAS, HILLE, ETGEN. CALCULUS, VOLUMEN II. REVERTE.
- SPIEGEL. MATEMATICAS AVANZADAS PARA INGENIERIA Y CIENCIAS. MC GRAW HILL (SERIE SCHAUM).
- UÑA, SAN MARTIN, TOMEO. PROBLEMAS RESUELTOS DE CALCULO EN VARIAS VARIABLES. THOMSON.

Additional Bibliography

- APOSTOL. CALCULUS. REVERTE.
- BRADLEY, SMITH. CALCULO DE VARIAS VARIABLES (VOLUMEN 2). PRENTICE HALL.
- BURGOS. CALCULO INFINITESIMAL DE VARIAS VARIABLES. MC GRAW HILL.
- LARSON, HOSTETLER, HEYD. CALCULO II. PIRAMIDE.
- LIASHKO, BOIARCHUK, GAI, GOLOVACH. ANTI-DEMIDOVICH (VOLUMENES 3 Y 4). URSS.
- STEWART,. CALCULO: CONCEPTOS Y CONTEXTOS. THOMSON.
- WREDE, SPIEGEL. CALCULO AVANZADO. MC GRAW HILL (SEIRE SCHAUM).
- ZILL, WRIGHT. CALCULO DE VARIAS VARIABLES. MC GRAW HILL . 2011