Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa
Public University of Navarre
| Course code: 178110 | 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 ] | ||||
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.
Learning outcomes
RA07: Understand the relationship between verbal, graphical, mathematical, and econometric analysis in the study of economics.
RA10: Derive relevant information from economic and social data that is difficult for non-professionals to recognize.
RA11: Use professional criteria for economic analysis, preferably those based on the use of technical instruments.
RA18: Work in a team, being able to argue their proposals and validate or reasonably refuse the arguments of others.
RA19: Organize work, in terms of good time management, order, and planning.
RA20: Select and generate the necessary information for each problem, analyze it, and make decisions based on it.
RA21: Value ethical, social, and environmental commitment in professional practice.
RA22: Continue learning in the future independently, deepening the knowledge acquired or starting in new areas of knowledge.
Methodology
- Theoretical sessions
- Practical sessions
- Individual or group work
- Tutorials
- Presentation and discussion of essays
- Performing exercises
- Personal study
- Exam
Evaluation
| Learning outcome |
Assessment activity |
Weight (%) | It allows test resit |
Minimum required grade |
|---|---|---|---|---|
| All | 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 |
| All | Regular assessment (individual): in which the students should solve problems or case studies | 60 | Yes, in the extraordinary assessment | No |
Agenda
1. ALGEBRA
1.1 Complex numbers.
1.2 Matrix diagonalization.
1.3 Quadratic forms.
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.
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.