Course: 2020/2021

Calculus II

(15493)

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 calculus of several variables underlying industrial technologies engineering.
2.- The ability to apply their knowledge and understanding to identify, formulate and solve mathematical problems of calculus of several using established methods.
3.- The ability to choose and apply relevant analytical and modelling methods in calculus of several variables.
4.- The ability to select and use appropriate tools and methods to solve mathematical problems in terms of calculus of several variables.
5.- The ability to combine theory and practice to solve mathematical problems of calculus of several variables.
6.- Understanding of the applicable methods and techniques applicable to calculus of several variables and their limitations.

Description of contents: programme

Chapter 1. n-dimensional Euclidean Space. Topologic structure. Functions of several variables.
Limits and continuity. Partial derivatives and differentiability. Gradient vector. Jacobian matrix. Chain rule and directional derivatives. Differential operators.
Chapter 2. Hessian matrix. Local extrema. Extremum problems with constraints.
Lagrange multipliers.
Chapter 3. Integration in R^n. Iterated integrals. Fubini's Theorem.
Change of variables. Applications.
Chapter 4. Line integrals. Conservative fields. Surface integrals.
Green, Stokes and Gauss' Theorems.

Learning activities and methodology

The learning activities will include:
1.- Master sessions.
2.- Problems sessions.
3.- Partial tests.
4.- Final exam.
5.- Tutorial activities.

Assessment System

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

Basic Bibliography

- DEMIDOVICH, B.P.. Problemas de Análisis Matemático,. Editorial Paraninfo. 1991
- SALAS, S. L. ; HILLE, E. ; ETGEN, G.. Calculus: one and several variables. Wiley. 2007
- MARSDEN, J.E. ; TROMBA, A.J.. Vector Calculus. Freemann. 2012

Additional Bibliography

- BURGOS, R.. Cálculo infinitesimal de una y varias variables. Mc-Graw Hill. 1995
- APOSTOL, T. . Calculus, Vol. 2. John Wiley & Sons. 1969
- BARTLE, R. G. . The Elements of Real Analysis,. John Wiley & Sons. 1976
- WREDE, R. C. ; SPIEGEL, M. R.. Schaum's Outline of Advanced Calculus. McGraw Hill. 2002