Guías Docentes Electrónicas
1. General information
ECTS credits:
Academic year:
10  17 
First quarter
Main language:
Second language:
Use of additional languages:
English Friendly:
Web site:
Lecturer: MARIA EMILIA GARCIA PEREZ - Group(s): 17 
Phone number
Office hours
Melchor de Macanaz/ 1.01
comprobar en campus virtual

Lecturer: GONZALO GARCIA-DONATO LAYRON - Group(s): 10  17 
Phone number
Office hours
Melchor de Macanaz/3.11
comprobar en campus virtual

2. Pre-Requisites

It is recommendable having taken the previous course Matemáticas I para la Economía and more concisely, the topics on Algebra: vector spaces, matrices, and quadratic forms and their classification. And on Calculus: dominium, continuity, derivatives and graphical representation of a function of a single variable; topology in the real line and integration methods.

3. Justification in the curriculum, relation to other subjects and to the profession

Matemáticas II para la economía is the second and last course about mathematics in the degree. This implies that it contains very important topics that are relevant in understanding great part of the rest of courses in the degree (and particularly those with a strong quantitative component). Matemáticas II is conceived to provide the student with the basic concepts of the analysis of several variables and an introduction to optimization methods.


In relation with professional skills, the main goal of the course is to introduce, from a mathematical perspective, the models and methods of quantitative analysis, including methods for decision making.

4. Degree competences achieved in this course
Course competences
Code Description
E03 Ability to find economic data and select relevant facts.
E06 Application of profesional criteria to the analysis of problems, based on the use of technical tools.
G01 Possession of the skills needed for continuous, self-led, independent learning, which will allow students to develop the learning abilities needed to undertake further study with a high degree of independence.
G03 Develop oral and written communication skills in order to prepare reports, research projects and business projects and defend them before any commission or group of professionals (specialised or non-specialised) in more than one language, by collecting relevant evidence and interpreting it appropriately so as to reach conclusions.
G04 Ability for the use and development of information and communication technology in the development of professional activity.
G05 Capacity for teamwork, to lead, direct, plan and supervise multidisciplinary and multicultural teams in both national and international environments.
5. Objectives or Learning Outcomes
Course learning outcomes
Enable student for autonomous work and learning, as well as for personal initiative
Train the student to listen to and defend arguments orally or in writing
Train the student to search for information in order to analyze it, interpret is meaning, synthesize it and communicate it to others.
Train the student to work out problems in creative and innovative ways.
To know the tools and methods for quantitative analysis of markets, sectors and companies, including models for decision-making and economic forecasting models.
Additional outcomes
Not established.
6. Units / Contents
  • Unit 1: The Rn space
    • Unit 1.1: Introduction and basic concepts
    • Unit 1.2: Basic topological aspects of Rn
  • Unit 2: Functions of several variables
    • Unit 2.1: Previous definitions
    • Unit 2.2: Limits and continuity
    • Unit 2.3: Derivatives and differentiability
  • Unit 3: Vectorial functions of several variables
    • Unit 3.1: Previous definitions
    • Unit 3.2: Limits and continuity
    • Unit 3.3: Derivatives and differentiability
  • Unit 4: Multiple integration
    • Unit 4.1: Multiple definite integration. Definition and properties
    • Unit 4.2: Double integrals over rectangular, type I and type II regions
    • Unit 4.3: Change of variables. Polar coordinates
  • Unit 5: Introduction to optimization problems
    • Unit 5.1: Introduction to modeling. Basic concepts of optimization problems
    • Unit 5.2: Types of problems. Classification of main methods to solve problems. Weirstrass theorem
    • Unit 5.3: Convexity analysis. Local-global theorem
  • Unit 6: Classic programming
    • Unit 6.1: Optimization without restrictions
    • Unit 6.2: Optimization subject to equality restrictions
  • Unit 7: Optimization subject to inequality restrictions
    • Unit 7.1: Standard form
    • Unit 7.2: Kuhn-Tucker conditions of optimality
7. Activities, Units/Modules and Methodology
Training Activity Methodology Related Competences ECTS Hours As Com R Description *
Class Attendance (theory) [ON-SITE] Lectures E03 G01 1.33 33.25 N N N
Class Attendance (practical) [ON-SITE] Problem solving and exercises E06 G01 0.67 16.75 N N N
Progress test [ON-SITE] Cooperative / Collaborative Learning E06 G01 G03 G04 G05 0.1 2.5 Y N N
Progress test [ON-SITE] Assessment tests G01 G03 0.1 2.5 Y N Y
Final test [ON-SITE] Assessment tests G01 G03 0.1 2.5 Y Y Y
Study and Exam Preparation [OFF-SITE] Self-study E03 E06 G01 G03 G04 1.4 35 N N N
Other off-site activity [OFF-SITE] Self-study G01 2 50 Y N Y
Other off-site activity [OFF-SITE] Problem solving and exercises G01 G04 0.2 5 Y N Y
Group tutoring sessions [ON-SITE] Group tutoring sessions G01 G03 G05 0.1 2.5 Y N Y
Total: 6 150
Total credits of in-class work: 2.4 Total class time hours: 60
Total credits of out of class work: 3.6 Total hours of out of class work: 90

As: Assessable training activity
Com: Training activity of compulsory overcoming
R: Rescheduling training activity

8. Evaluation criteria and Grading System
  Grading System  
Evaluation System Face-to-Face Self-Study Student Description
Assessment of problem solving and/or case studies 20.00% 0.00% Activities to be solved in groups of three to four students. There have been programmed three of these activities: the first one with a weight of 10% and each of the two others with a 5% weight.
Progress Tests 10.00% 0.00% A midterm individual exam to evaluate the progress of the student with a weight of 10%. This exam covers the units 1,2 and 3.
Final test 70.00% 0.00% A final exam with a weight of 70%
Total: 100.00% 0.00%  

Evaluation criteria for the final exam:
Evaluation criteria not defined
Specifications for the resit/retake exam:
For the resit evaluation the students will have an exam that counts 80% and the remaining 20% is obtained in the following way: 10% in an extra activity proposed by the teacher before the exam and 10% that corresponds to half the grade in the group activities during the regular period.
Specifications for the second resit / retake exam:
Evaluation criteria not defined
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours

Unit 1 (de 7): The Rn space
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 33.25
Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] 16.75
Progress test [PRESENCIAL][Cooperative / Collaborative Learning] 2.5
Progress test [PRESENCIAL][Assessment tests] 2.5
Final test [PRESENCIAL][Assessment tests] 2.5
Study and Exam Preparation [AUTÓNOMA][Self-study] 35
Other off-site activity [AUTÓNOMA][Self-study] 50
Other off-site activity [AUTÓNOMA][Problem solving and exercises] 5
Group tutoring sessions [PRESENCIAL][Group tutoring sessions] 2.5

Global activity
Activities hours
10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
Apostol, T.M. Calculus. Vol. 1 y Vol 2. (2a edición). Reverte. 1994  
Barbolla, R.; Cerdá, E. y Sanz, P. Optimización Prince-Hall. 2001  
Besada, M., García, F.J., Miras, M.A. y Vázquez, C. Cálculo de varias variables. Cuestiones y ejercicios resueltos Prentice Hall 2001  
Caballero, R.E., Calderón, S., Galache, T.P., González, A.C., Rey, M.L. y Ruiz, F. Matemáticas aplicadas a la economía y la empresa. 434 ejercicios resueltos y comentados Ediciones Pirámide 2000  
Chiang, A.C. and Wainwright, K. Fundamental Methods of Mathematical Economics McGraw-Hill 2005  
Fuente, A. Mathematical methods and models for economists. Cambridge University Press. 2000  
Guzmán, L., Sánchez, M., Muñoz, A. y Santos, J. Fundamentos matemáticos para la administración y dirección de empresas. Análisis y Optimización Editorial Centro de Estudios Ramón Areces, S.A. 1999  
Martín, Q.; Santos, M.T. y De Paz, Y. Investigación operativa Pearson Prentice-Hall. 2005  
Purcell, E.J. y otros Cálculo. (8a edición). Prentice-Hall. 2001  
Stewart, J. Cálculo multivariable. (4a edición). Thomson. 2002  
Uña, I., San Martín, J. y Tomeo, V. Problemas resueltos Thomson. 2007  

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