Academic year: 2018/2019

Course code: 174104 |
Subject title: MATHEMATICS |
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Credits: 6 |
Type of subject: Basic |
Year: 1 |
Period: 1º S |
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Department: Estadística, Informática y Matemáticas |
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Lecturers |
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INDURAIN ERASO, ESTEBAN | DE MIGUEL VELASCO, JUAN R. (Resp) |

- CG03: Oral and written communication in their mother tongue.
- CG05: Computer skills relevant to the field of study.
- CG07: The capacity to solve problems.
- CG09: The capacity to work as part of a team.
- CG16: Working in high-pressure environments.
- CG17: A capacity for self-reliant learning.

- CE03: To discern relevant information and data in microeconomic and macroeconomic data which a non-professional would be unable to recognise.
- CE04: To perform economic analysis applying professional criteria, preferably criteria based on the use of technical instruments.

- R_MC_03: Understand and know how to apply the basic elements of linear algebra and differential and integral calculus to solve economic and business problems.
- R_MC_07: Use appropriate computer programs for the treatment of data or for the resolution of analytical problems.
- R_MC_10: Develop the right attitude to understand and be able to use new quantitative techniques that may be necessary in the exercise of the profession.

- Theoretical sessions
- Practical sessions
- Individual or group work
- Tutorials
- Presentation and discussion of essays
- Performing exercises
- Personal study
- Exam

Training activity | Methodology | Proficiencies developed |

Theoretical sessions | Lecture focused on explaining concepts illustrated with examples | CG03, CE03, CE04 |

Practical sessions | Realization of classroom exercises in small groups (4 people). Problems will be resolved preferably in an economic environment using, when deemed advisable, computing tools. Practices with the field of microeconomics. Oral presentation of the results. | CG03, CG05, CG07, CG09, CG16, CB2, CE03, CE04 |

Preparation of assignments, individually or in groups. | Exercises and problems with non-presential character work. Sometimes individual and sometimes work in group. | CG03, CG05, CG07, CG09, CG16, CB1, CE03, CE04 |

Individualized tutoring or in small groups | Working sessions customized teacher-student or between the teacher and a reduced group of students. | CG07, CG09, CB1,CB3,CB4 |

Personal study and examination. | CG03, CG07, CG16, CG17, CB5, CE03, CE04 |

Learning outcome | Evaluation Method | Weight (%) | Recoverable |

R_MC_03, R_MC_07, R_MC_10 | Continuous assessment: active participation in the course, tests of control and working in groups, individually or in small groups | 40 | No |

R_MC_03, R_MC_10 | Regular assessment (individual): in which the students should solve problems or case studies | 60 It is compulsory to get at least 4 points (up to 10) in order to pass this subject matter | Yes |

Differential calculus: a study of the functions of one and several variables, properties, operations, graphical representations, continuity, differentiability, asymptotic behavior. Homogeneous functions. Optimization, extreme of functions of one and several variables, unconstrained optimization, optimization with equality constraints. Integral calculus: indefinite and definite integral. Calculation of primitives. Applications to the calculation of areas and other applications. Matrices, determinants, operations and applications: Matrix calculus. Discussion and solving of systems of linear equations. Applications to Economics and Business Models.

1. MATRIX CALCULUS (LINEAR ALGEBRA)

1.1. Matrices

1.2. Transpose of a matrix

1.3. Addition of matrices.

1.4. Product of a matrix by a scalar number.

1.5. Product of matrices.

1.6. Inverse matrices.

1.7. Elementary transformations of a matrix.

1.8. Successive powers of a matrix.

1.9. Determinants

1.10. Determinants and inverse matrices.

1.11. Rank of a matrix.

1.12. Systems of linear equations.

2. DIFFERENTIAL CALCULUS

2.1. The real line and the n-dimensional space.

2.2. Real functions.

2.3. Limits.

2.4. Continuity.

2.5. Derivatives (functions of a single real variable).

2.6. Partial derivatives (functions of several real variables).

2.7. Optimization (functions of a single real variable).

2.8. Concave and convex functions.

2.9. Optimization without constraints (functions of two real variables).

2.10. Optimization with constraints.

3. INTEGRAL CALCULUS

3.1. Primitive integral of a real function.

3.2. Definite integral.

4: APPENDICES

4.1. Homogeneous functions.

4.2 Optimization theory (functions of several real variables).

**Acceda a la bibliografía que su profesor ha solicitado a la Biblioteca.**

By means of the tool "MiAulario", the students will have access to schemes, lists of exercises, links to complementary material, etc., related to the subject matter.

We do not recommend any particular textbook on this subject. There are many possible books on Differential Calculus, Integral Calculus, Linear Algebra and related items, even from a point of view of Economics or reportedly addressed to students of Economics and/or Business Administration, that can be found in any "average-size" universitary library.

Perhaps the reference "Mathematical models in the Social, Management ald Life Sciences", by D.N. Burghes and A. D. Wood (Ellis Horwood. Chichester, UK. 1984) is an excellent reference to find "case-studies" related to the main concepts to be developed throughout the semester in this subject matter.

For the sake of completeness, we include below a list (not exhaustive, and by no means the only possible one) of texts in Spanish that can be used in the preparation of some lectures.

LIST (texts in Spanish) FOLLOWS:

- Arya, Jagdish C.; Lardner, Robin W. (2005) "Matemáticas Aplicadas a la Administración y la Economía" (5ª edición) Pearson Educación.
- Baum, A. (1992) "Cálculo aplicado" Limusa.
- Caballero, R. y otros (1993) "Matemáticas aplicadas a la economía y a la empresa (380 ejercicios resueltos y comentados)" Pirámide.
- Calvo y otros (2003) "Problemas resueltos de matemáticas aplicadas a la Economía y la Empresa" Paraninfo.
- Canceló, J.R. y otros (1987) "Problemas de álgebra lineal para economistas" Tebar Flores.
- García Güemes, A. (1992) "Matemáticas aplicadas a la Empresa" A.C.
- Hoffman, L.D. y Bradley, G.L. (1998) "Cálculo aplicado a Administración, Economía y Ciencias Sociales" (6ª edición) McGraw-Hill.
- Martínez Estudillo, F. J. (2005) "Introducción a las Matemáticas para la Economía" Desclée de Brouwer.
- Muñoz Alamillos, A. y otros (2003) "Problemas de matemáticas para economía, administración y dirección de empresas" Ediciones Académicas.
- Sammamed y otros "Matemáticas I. Economía y Empresa. Problemas" Centro de Estudios Ramón Areces.
- Vázquez Cueto, J.M. (2002) "Matemáticas Empresariales: Ejercicios planteados y resueltos" CEURA.