## Public University of Navarre

Academic year: 2024/2025 | Previous academic years:  2023/2024  |  2022/2023  |  2021/2022  |  2020/2021
 Course code: 176206 Subject title: MATHEMATICS II Credits: 6 Type of subject: Mandatory Year: 1 Period: 2º S Department: Estadística, Informática y Matemáticas Lecturers: CAMPION ARRASTIA, MARÍA JESÚS (Resp)   [Mentoring ] PERALES BARRIENDO, JULEN   [Mentoring ]

Partes de este texto:

### Module/Subject matter

Module: Quantitative methods. Subject matter: Mathematics.

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### Contents

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.

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Not applicable.

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Not applicable.

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### Methodology

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

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### Evaluation

Learning
outcome
Assessment
activity
Weight (%) It allows
test resit
Minimum
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 Yes, in the extraordinary assessment No
R_MC_03, R_MC_10 Regular assessment (individual): in which the students should solve problems or case studies 60 Yes, in the extraordinary assessment No

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### Agenda

1. ALGEBRA

1.1 Complex numbers.

1.2 Matrix diagonalization.

2. DYNAMICAL SYSTEMS (GENERAL THEORY)

2.1 Preliminary concepts on dynamical systems.

2.2 Differential equations.

2.3 Systems of linear differential equations.

3. DISCRETE DYNAMICAL SYSTEMS

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.

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### Bibliography

Access the bibliography that your professor has requested from the Library.

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.

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English.

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Location details

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