Course guide of Mathematics for Economics II (2261125)

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).

• 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

• 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.

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.

Exercises about the lessons described in Theory Syllabus

• 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

• 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.

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

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.

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

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)

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)