Course: 2024/2025

Calculus II

(13491)

Requirements (Subjects that are assumed to be known)

Calculus I
Linear Algebra

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.

Skills and learning outcomes

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.
- The use of Artificial Intelligence tools is not allowed in this course.

Assessment System

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

Calendar of Continuous assessment

Extraordinary call: regulations

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

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