Universidad Rey Juan Carlos Facultad de CC. Jurídicas y Sociales. Licenciatura en ADMINISTRACIÓN Y DIRECCIÓN DE EMPRESAS (BILINGÜE) asignatura:

Transcripción

1 Universidad Rey Juan Carlos Facultad de CC. Jurídicas y Sociales (Campus de Vicálvaro) Licenciatura en ADMINISTRACIÓN Y DIRECCIÓN DE EMPRESAS (BILINGÜE) asignatura: MATHEMATICS curso y duración: FIRST YEAR FIRST TERM carácter y créditos: COMPULSORY 7,5 área de conocimiento: profesores responsables del programa: ESTADÍSTICA Y MATEMÁTICAS JUAN JOSÉ RIENDA GÓMEZ vigencia de este programa, desde: 01/10/05

2 MATHEMATICS DEGREE IN BUSINESS ADMINISTRATION SOCIAL AND LAW SCIENCES FACULTY KING JUAN CARLOS UNIVERSITY COMPULSORY FIRST YEAR FIRST TERM CREDITS: 7.5 ACADEMIC YEAR: SPECIFIC OBJECTIVES SUBJECT PROGRAM To reinforce previous mathematical concepts and to make progress with some new knowledge, methods and techniques of analyses, deepening in scientific rigor, reasoning and intuition. To bring the mathematical reasoning closer to economic analysis. To provide students with the main mathematical knowledge to be capable of using them in other subjects. To promote the use of mathematical software in class. FIRST PART: LINEAR ALGEBRA. CHAPTER 1. VECTOR SPACES. Previous knowledge Vector Space: Definition and consequences Specific concepts of vectorial space Vector subspaces Linear transformations CHAPTER 2. LINEAR TRANSFORMATIONS. LINEAR SEQUENTIAL PROCESSES Linear transformations: Eigenvalues and eigenvectors Similar matrices: Diagonalization of a square matrix Linear sequential processes CHAPTER 3. REAL QUADRATIC FORMS Definition of a real quadratic form

3 Quadratic forms classification Diagonal expressions. Inertia law. Study of a quadratic form sign SECOND PART: DIFFERENTIAL CALCULUS. CHAPTER 4. ANALISIS OF MAGNITUDES VALUED BY A FUNCTION Magnitudes assessment Different ways to express assessment Economic magnitudes valued at an explicit way Objectives of analysis CHAPTER 5. LIMITS OF FUNCTIONS. CONTINUOUS BEHAVIOUR Intuition of continuous behaviour n Topologic notions in R space Finite limit in one point. Restricted limits Continuous behaviour Discontinuities and trends in real functions of one variable Indeterminations CHAPTER 6. DERIVATIVES. BEHAVIOUR ANALYSIS. MARGINALS VALUES. ELASTICITIES. Behaviour and local trend in one direction Behaviour analysis and local trend in a real function of one variable. Derivatives Derivatives rules Behaviour analysis and local trend, in one given direction, of real function of several variables. Directional derivatives Partial derivatives matrices Behaviour assessments of economic functions. Marginal values. Elasticities CHAPTER 7. DIFFERENTIATION. MAXIMUM AND MINIMUM VALUES IN SEVERAL VARIABLES FUNCTIONS Local behaviour in several variables. Inadequacies of derivability Differentiability: Definition. Properties Real differentiable twice function of n variables Differential on one point Differential s expression according to differentials of variables Differentiability sufficient condition. Functions of type 1 2 C, C,... Schwartz theorem. Relative extreme points in several free variables.

4 CHAPTER 8. OPTIMISATION WITH EQUALITY RESTRICTIONS Programming with equality restrictions Method of Lagrange multipliers Sufficient condition Economic explanation of Lagrange multipliers Economic applications CHAPTER 9. COMPOUND FUNCTIONS. HOMOGENEOUS FUNCTIONS. IMPLICITS FUNCTIONS Derivatives of compound functions. Chain rule. Homogeneous function: Definition and properties Homogeneous production s function. Scale returns Real implicit function of one variable Real implicit function of several variables Marginal relations of substitution THIRD PART: ANALYSIS OF MAGNITUDES ON DISCREET TIME. CHAPTER 10. NUMERICAL SUCCESSION. RECURRENT EQUATIONS. DYMANIC ANALYSIS BY PERIODS. Numerical successions: Definition and meanings. Different ways to establish a succession Analysis from a general term Analysis from a recurrent equation Applications to dynamic economic analyses by periods CHAPTER 11. NUMERICAL SERIES. DISCREET DISTRIBUTIONS Distributed into discreet time magnitudes Finite series. Geometrical series Infinite series FOURTH PART: INTEGRAL CALCULUS, CONTINUOUS DYNAMIC ANALYSIS. CHAPTER 12. CALCULUS OF PRIMITIVES Magnitudes valued by a differential equation Direct integration method Integration by parts Integration of rational functions Integration by t-substitution

5 CHAPTER 13. DIFFERENTIAL EQUATIONS. CONTINUOUS DYNAMICAL ANALYSIS First-order differential equations Separable in variables differential equations Homogeneous differential equations Linear differential equations Economic applications of differential equations CHAPTER 14. DEFINITE INTEGRALS Magnitudes distributed by a continuous way (one variable) Riemann Integrals Definite Integrals. Theorems of integral Calculus CHAPTER 15. IMPROPER INTEGRALS. EULERIAN INTEGRALS Non-defined interval s improper integrals Non-defined function s improper integrals Gamma integrals. Beta integrals. CHAPTER 16. DOUBLE INTEGRALS Magnitudes distributed according to two variables Integration conditions Marginal density s functions. Reiterative integration T-substitutions. BIBLIOGRAPHY BASIC BALBAS, A.; GIL FANA, J.A.; GUTIERREZ, S. Análisis Matemático para la Economía II. Madrid: A. C., CÁMARA, A; GARRIDO, R.; TOLMOS, P. Matemáticas para la Empresa. Ejercicios resueltos. Colección Paso a Paso. Madrid: Thomson, CÁMARA, A.; GARRIDO, R.; TOLMOS, P. Curso Básico de Matemáticas para el acceso a la Universidad. Delta Publicaciones GUTIERREZ, S; FRANCO, A. Matemáticas aplicadas a la Economía y a la Empresa. Madrid: A. C., ADDITIONAL BARBOLLA, R; SANZ, P: Álgebra Lineal y Teoría de Matrices. Madrid: Prentice Hall, 1998.

6 CALVO, M.E. et al. Problemas Resueltos de Matemáticas Aplicadas a la Economía y a la Empresa. Madrid: Thomson, FERNÁNDEZ, C.; VÁZQUEZ, F.J.; VEGAS, J.M. Cálculo Diferencial de Variables Variables. Madrid: Thomson, HERAS, A; VILAR, J.L. Problemas de Álgebra Lineal para la Economía. Madrid: A. C., SANZ, P.; VÁZQUEZ, F.J.; ORTEGA, P. Álgebra Lineal: Cuestiones, Ejercicios y Tratamiento en Derive (Incluye Diskette). Madrid: Prentice Hall, SYDSAETER, K.; HAMMOND, P. Matemáticas para el Análisis Económico. Madrid: Prentice Hall, VILAR, J.L. et al. Cálculo Diferencial para la Economía. Madrid: A. C., 1993