Course guide of Mathematics for Economics II (2261125)

Curso 2024/2025
Approval date: 20/06/2024

Grado (bachelor's degree)

Bachelor'S Degree in Economics

Branch

Social and Legal Sciences

Module

Ampliación de Matemáticas

Subject

Matemáticas para la Economía II

Year of study

2

Semester

1

ECTS Credits

6

Course type

Compulsory course

Teaching staff

Theory

Lidia Fernández Rodríguez. Grupo: A

Practice

Lidia Fernández Rodríguez Grupos: 1 y 2

Timetable for tutorials

Lidia Fernández Rodríguez

Email
  • First semester
    • Wednesday
      • 10:30 a 11:00 (Despacho B03 Fcee)
      • 12:00 a 14:30 (Despacho B03 Fcee)
    • Thursday de 12:00 a 14:00 (Despacho 48 Facultad de Ciencias)
    • Friday de 12:30 a 13:30 (Despacho B03 Fcee)
  • Second semester
    • Monday de 17:00 a 18:00 (Despacho 48 Faclutad de Ciencias)
    • Tuesday
      • 09:30 a 13:30 (Despacho 48 Facultad de Ciencias)
      • 17:00 a 18:00 (Despacho 48 Facultad de Ciencias)

Prerequisites of recommendations

Completion of the following courses: Mathematics and Mathematics for Economics I (Bachelor’s Degree in Economics) or Mathematics for Business (Bachelor’s Degree in Business).

Brief description of content (According to official validation report)

  • Mathematical programs with equality constraints. Method of Lagrange multipliers. Economical applications.
  • Mathematical programs with inequality constraints. Karush-Kuhn-Tucker conditions. Economic interpretation of the multipliers.
  • Linear programming. Simplex algorithm. Sensibility and post-optimization analysis.
  • Differential and difference equations of greater order. Stability criteria

Objectives (Expressed as expected learning outcomes)

  • Solve mathematical programs with equality constraints using substitution method and Lagrange multipliers.
  • Aply Karush-Kuhn-Tucker multipliers method to solve programs with inequality constraints.
  • Understand the economical interpretation of the multipliers.
  • Know the utility of Weierstrass theorem and the implication of coercivity to guarantee the existence of solution in optimization problems.
  • Recognize quadratic functions and separate variables functions which are coercive.
  • Aply simplex method to solve linear programs.
  • Solve problems of production planification, diet, etc.
  • Analize sensitivity in a linear program.
  • Solve linear difference equations.
  • Solve linear differential equations.
  • Know stability criteria for dynamical systems.

Detailed syllabus

Theory

Lesson 1. Ordinary differential equations.

  • Phase portrait for autonomous differential equations.
  • Linear differential equations.
  • Stability.

Lesson 2. Ordinary Difference equations.

  • Autonomous difference equations.
  • Linear difference equations.
  • Stability.

Lesson 3. Linear programming.

  • Simplex method.
  • Two phases simplex method.
  • Economical applications: Diet problem and production problem.
  • Sensitivity analysis.

Lesson 4. Optimization with equality constraints.

  • Weierstrass theorem.
  • Coercive functions.
  • Method of Lagrange multipliers.
  • Interpretation of the multipliers.

Lesson 5. Optimization with inequality constraints.

  • Method of the Karush-Kuhn-Tucker multipliers.
  • Interpretation of the multipliers.

Practice

Exercises about the lessons described in Theory Syllabus

Bibliography

Basic reading list

  • ARRANZ PEREZ, GARCILLAN Y OTROS, Ejercicios resueltos de Matemáticas para la Economía. Optimización y Operaciones financieras. Ed. AC, 1998.
  • ÁLVAREZ DE MORALES, M. Y FORTES, M. A., Matemáticas Empresariales. Ed. GodelImpresiones Digitales S.L., 2009.
  • GANDOLFO, G., Economic Dynamics, ED. Springer, 2010.
  • GARCIA, J., MARTINEZ, C. Y RODRIGUEZ M.L., Optimización Matemática aplicada a la Economía. Ed.Godel Impresiones Digitales S.L., 2009.
  • STEWART, J. Multivariable Calculus. Cengage Learning, 2012.
  • SYDSATER, K Y HAMMOND, P. J., Further Mathematics for Economic Analysis Ed. Prentice Hall. 2008.
  • SYDSATER, K Y HAMMOND, P. J., Essential Mathematics for Economic Analysis Ed. Prentice Hall. 2016.
  • ZILL, D.G. Ecuaciones diferenciales con Aplicaciones. Ed. Grupo Iberoamérica. 1988

Complementary reading

  • ALEGRE, P. Y OTROS, Ejercicios resueltos de Matemáticas Empresariales 2. Ed. AC,1993.
  • BARBOLLA, S., CERDÁ, E. Y SANZ, P., Optimización (cuestiones, ejercicios y aplicaciones a la economía). Ed. Prentice Hall 2000.
  • BORRELL, J., Métodos matemáticos de la Economía: Programación matemática. Ed. Pirámide, 1987.
  • CABALLERO, R., CALDERON, S. Y OTROS, Matemáticas aplicadas a la economía y a la empresa. Ed. Pirámide, 1993.
  • CHIANG, Métodos fundamentales en Economía Matemática. Ed. McGraw-Hill, 2006.
  • DIAZ, A., NOVO, V. Y PERÁN, J., Optimización. Casos prácticos. UNED Ediciones, 2000.
  • GARCÍA CABELLO J., Cálculo Diferencial de las Ciencias Económicas. Ed. Delta Publicaciones 2008.
  • GASS, S.I, Programación lineal. Ed. Cecsa, 1978.
  • HAEUSSLER, E. Y PAUL, E., Matemáticas para la Administración, Economía, Ciencias Sociales y de la Vida. Ed.Prentice Hall, 1997.
  • PERIS, J.E. Y CARBONELL, L., Problemas de matemáticas para economistas. Ed. Ariel Economía, 1986.
  • SOTO, M.D., Métodos de Optimización. Ed. Delta publicaciones, 2007.

Recommended links

  • Teaching platform PRADO: https://prado.ugr.es/
  • Web site of the Department of Applied Mathematics: http://mateapli.ugr.es/

Assessment methods (Instruments, criteria and percentages)

Ordinary assessment session

According to University of Granada Assessment and Grading Regulations (see http://secretariageneral.ugr.es/bougr/pages/bougr71/ncg712/!), continuous and single final assessment are proposed for this subject.

Continuous assessment will be the default choice, unless another option be formally requested to the Head of the Department (University of Granada Assessment and Grading Regulations).

Continuous assessment is divided into two blocks. The score of each block is obtained by gathering the score of a partial test and other activities such as exercises, online tests, seminars/workshops, blackboard exhibitions, homeworks, etc. The breakdown of the grades is the following:

  • Block I, related with lessons 1 and 2, will score 4 points maximum.
  • Block II, related with lesson 3, 4 and 5, will score 6 points maximum.

The final grade will be:

  • The sum of both block grades if this is greater than or equal to 5 points.
  • If the sum is less than 5 points, students could make an exam of the blocks where the obtained mark is less than 50% of the maximum score (2 points in Block I, and 3 points in Block II). The final exam will consist of a global test comprising both blocks mentioned before with the same score (that is, Block I with maximum score 4 points and Block II with 6 points).
  • If a student takes the part corresponding to one block in the final test, the student drops the previous score in this block. The grade obtained in each block in the final test will substitute the one obtained during the semester. The final grade will be the sum of both block marks.

Extraordinary assessment session

A single final test on the theoretical and practical contents of the course with a maximum score of 10 points.

Single final assessment

The single final assessment will comprise a single test with a maximum score of 10 points. Every detail on the single final assessment regulations by UGR can be found at the following URL: http://secretariageneral.ugr.es/bougr/pages/bougr112/_doc/examenes%21.

Date and place of the exam will be set by the Faculty (as well as the final exam in the continuous assessment)

Additional information

All aspect related with both continuous and final assesment will be guided by current assessment regulations by UGR
(http://secretariageneral.ugr.es/bougr/pages/bougr112/_doc/examenes%21)

Información de interés para estudiantado con discapacidad y/o Necesidades Específicas de Apoyo Educativo (NEAE): Gestión de servicios y apoyos (https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad).

Software Libre

No