Checking date: 21/02/2022

Course: 2022/2023

Calculus II
Study: Bachelor in Telecommunication Technologies Engineering (252)


Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS


Branch of knowledge: Engineering and Architecture

Requirements (Subjects that are assumed to be known)
Calculus I Linear Algebra
The aim of this course is to provide students the basic tools of differential and integral calculus of several variables. To achieve this goal students must acquire a range of expertise and capabilities. SPECIFIC LEARNING OBJECTIVES: - To understand the n-dimensional Euclidean space and in more depth n = 2 and 3. - To know the properties of scalar and vector functions of several variables. - To understand the concepts of continuity, differentiability and integrability. - To be able to handle optimization problems using optimization techniques. - To understand how to calculate double, triple, line and surface integrals. - To know and apply the main theorems of vector calculus: Green, Gauss, Stokes. - To understand how to apply the integral to calculate surface areas, volumes and solve some basic problems of Mathematical-Physics. SPECIFIC ABILITIES: - To be able to work with functions of several variables given in terms of a graphical, numerical or analytical description. - To understand the concept of differentiable function and ability to solve problems involving the concept. - To understand the concept of multiple integral, line and surface integral and its practical applications. GENERAL ABILITIES: - To understand the necessity of abstract thinking and formal mathematical proofs. - To acquire communicative skills in mathematics. - To acquire the ability to model real-world situations mathematically, with the aim of solving practical problems. - To improve problem-solving skills.
Skills and learning outcomes
Description of contents: programme
1 .- The n-dimensional Euclidean space. Cartesian, polar, cylindrical and spherical coordinates. 2 .- Scalar and vector functions of several variables. Limits, continuity and differentiability. 3 .- Taylor's theorem. Optimization problems with and without constraints. 4 .- Double, triple, line and surface integral. 5 .- Theorems of Green, Gauss, Stokes and its applications .
Learning activities and methodology
Lecture sessions: 3 ECTS credits Problem sessions: 3 ECTS credits
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Calendar of Continuous assessment
Basic Bibliography
  • HERNANDO, P. J.. Clases de Cálculo II para Ingeniería. Versión 3.6, PDF. 2021
  • Howard Anton, Irl C. Bivens, Stephen Davis,. Calculus Multivariable, 9th ed.,. Wiley. & Sons.. 2009
  • Jarrold E. Marsden, Anthony Tromba.. Vector Calculus, 6th ed.. W. H. Freeman.. 2013
  • Lasrson, R., Edwards, B. Calculus, 10th International ed.. Brooks Cole, Cengage Learning. 2014
  • P. J. Hernando. Clases de Cálculo II para Ingeniería. Revisión 2.5. 2018
  • Salas, S., Hille, E., Etgen, G.. Calculus: one and several variables, 10th ed.. Wiley. 2007
  • Stewart, James. Calculus, 8th ed.. Cengage Learning. 2016
  • Weir, Maurice D., Hass, Joel, Thomas, George B . Jr.. Multivariable Thomas'calculus. Pearson Addison Wesley. 2014
Additional Bibliography
  • James Stewart. Multivariable Calculus: Concepts and Contexts. Cengage Learning. 2009
  • James Stewart. Multivariable Calculus: Concepts and Contexts, 4 ed.. Brooks/Cole, Cengage Learning. 2010
  • Juan de Burgos. Cálculo infinitésimal de varias variables, 2 ed.. Mc Graw-Hill Interamericana. 2008
  • Paul Charles Matthews. Vector Calculus. Springer. 1998
  • Ron Larson, Bruce H. Edwards, Robert P. Hostetler.. Multivariable Calculus. Cengage Learning. 2006

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