Course: 2022/2023

Calculus II

(15367)

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

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.