Public University of Navarre

Academic year: 2019/2020 | Previous academic years:  2018/2019  |  2017/2018  |  2016/2017  |  2015/2016 
International Double Bachelor's degree in Economics, Management and Business Administration at the Universidad Pública de Navarra
Course code: 176206 Subject title: MATHEMATICS II
Credits: 6 Type of subject: Mandatory Year: 1 Period: 2º S
Department: Estadística, Informática y Matemáticas

Partes de este texto:


Module/Subject matter

Module: Quantitative methods. Subject matter: Mathematics.



Intermediate Differential Calculus, Integral Calculus and Linear Algebra.


General proficiencies

  • 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.


Specific proficiencies

  • 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.


Learning outcomes

  • 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


Relationship between formative activities and proficiencies

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



Diagonalization of square matrices: eigenvectors and eigenvalues, characteristic polynomial, diagonalizable matrices. Quadratic forms: polynomial and matrix expression, symmetrical matrices Diagonalization. Convergence and geometric series: convergence of successions, geometric series, criteria of convergence of series, sum of series. Introduction to dynamic models: differential equations, difference equations.




1.1 Complex numbers.

1.2 Matrix diagonalization.

1.3 Quadratic forms.


2.1 Preliminary concepts on dynamical systems.

2.2 Differential equations.

2.3 Systems of linear differential equations.


3.1 Sequences of real numbers.

3.2 Series of real numbers.

3.3 Difference equations: the linear case.

3.4 Systems of linear difference equations.



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, Differential Equations, Dynamical Systems, Difference Equations 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 and 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:

  • Balbás, A. y otros (1998) "Análisis matemático para la Economía II". A C Madrid.
  • Chiang, A. C. (1987) "Métodos fundamentales de economía matemática". McGraw-Hill. Madrid.
  • Fernández Pérez, G. y otros (2003) "Ecuaciones diferenciales y en diferencias: sistemas dinámicos". Thomson.
  • Lomelí, H. y Rumbos, B. (2003) "Métodos dinámicos en economía". Thomson.
  • Martínez Estudillo, F. J. (2005) "Introducción a las Matemáticas para la Economía" Desclée de Brouwer.
  • Takahashi, T. (1991) "Ecuaciones en diferencias con aplicaciones". Grupo Editorial Iberoamericana.