Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa
Public University of Navarre
| Course code: 177106 | Subject title: MATHEMATICS | ||||
| Credits: 6 | Type of subject: Basic | Year: 1 | Period: 1º S | ||
| Department: Estadística, Informática y Matemáticas | |||||
| Lecturers: | |||||
| GOICOECHEA LOPEZ-VAILO, M. ISABEL (Resp) [Mentoring ] | CAMPION ARRASTIA, MARÍA JESÚS [Mentoring ] | ||||
| PERALES BARRIENDO, JULEN [Mentoring ] | |||||
Contents
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.
Learning outcomes
RA01: Identify relevant economic information sources for the company and their content.
RA02: Understand economic institutions as the result and application of theoretical or formal representations of how the economy works.
RA03: Derive relevant information for the company from data that cannot be recognized by non-professionals.
RA20: Plan, organize, and control global management projects or those of the different functional areas of the company.
RA25: Use personal, social, and methodological knowledge, skills, and abilities to issue advisory reports on specific situations of companies and markets.
RA29: Develop the skills necessary to understand and apply quantitative techniques to the interpretation and resolution of socioeconomic problems.
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 |
|---|---|---|---|---|
| Continuous assessment: active participation in the course, tests of control and working in groups, individually or in small groups. | 40 | Yes, in the resit assessment. | No | |
| Regular assessment (individual): in which the students should solve problems or case studies. | 60 | Yes, in the resit assessment. | No |
Agenda
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).
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 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.