Checking date: 10/07/2020

Course: 2020/2021

Calculus II
Study: Bachelor in Industrial Technologies Engineering (256)

Coordinating teacher: COLORADO HERAS, EDUARDO

Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS


Branch of knowledge: Engineering and Architecture

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

The course syllabus and the academic weekly planning may change due academic events or other reasons.