Obligatory: Not established
Recomended: Since mathemtics is a subject where concepts and proceedings are all related with each other, it would be convenient to have a solid basis from high school. In particular, it is convenient the knowledge of;
Algebraic expresions: integer algebraic operations; Ruffini's rule; factor decomposition of algebraic expresions; fraction simplification; basic algebraic structures.
·Radicals: Reduction to common index radicals; fractial exponents, extraction e introduction of factors; operations with radicals.
·Inequalities: Geometric resolution.
-Progressions: arithmetic progressions, geometric prograssions.
·Real valued functions: Domain and continuity; derivability and diferenciability: graphic representation of functions.
·Trigonometry: angles; trigonometric functions; graphic respresentation of trigonometric functions; trigonometric equivalences;trigonometric inverse functions.
·Logarithms and exponential functions.
·Introduction to elemental derivation.
Mathematics I for business is parte of the Cuantitative Methods for Business modulus. Therefore, it is an essential subject for many others subjects in the Degree.
Mathematical concepts never appear isolated but based on previous definitions. Therefore, it is difficult to understand any content without understanding the previous lesson. Thus, the success in studying mathematics is based on having a general vision of the subject giving context to each new concept which can not be learnt isolated.
The first part, devoted to linear algebra, gives the basi knowlege for a great part of economic theory models. The second part, devoted to one variable calculus will be the basis for the basic functions used in enocomy such as offer and demand functions.
It must be considered that mathematics are an instrumental subject for the rest of specidic subjects in the degree since it is applied in many areas of business and economy. However, although is not considered as a pure object of study, the subject is developed with all due rigour and formality to allow the students to pursue futur PhD studies in economics.
In relation with the profession it is worth noting that the aim of this subject is to know the models and techniques of cuantitative analisys in business including the models for decission making in business and economic forecast.
|E07||Understand the economic environment as a result and application of theoretical or formal representations on how the economy works. To do so, it will be necessary to be able to understand and use common handbooks, as well as articles and, in general, leading edge bibliography in the core subjects of the curriculum.|
|E11||Know the workings and consequences of the different economic systems|
|G01||Possession of the skills needed for continuous, self-led, independent learning, which will allow students to develop the learning abilities needed to undertake further study with a high degree of independence.|
|Course learning outcomes|
|Know the tools and methods for the quantitative analysis of the company and its environment, including models for business decision making as well as economic forecast models.|
|Work out problems in creative and innovative ways.|
|1.- Being capable of proposing, studying and solving a linear system. To do this: 1.1.- Knowing the different types of matrices and operate with them. 1.2.- Being able to calculate the determinant and the inveres of a matix. 1.3.- Proposing linear systems from real situations and deciding if the system has a solution or not. In case it has a solution, being able to find it. 2.- Given a linear map representing certain economic sitution, being able to find the corresponding matrix and, if possible, present it in the most simple way (diagonal). To do this: 2.1.- The student should be familiar with the vector space Rn and be capable of givin a base for it. 2.2.- The student will know the different linear maps and how to operate with them. 2.3.- Stablish an isomorphism between linear maps and matrices. 2.4.- Being able to calculate the eigenvalues and eigenvectors of a matrix. 2.5.- Finding the diagonalization of a matirx. 3- Computing cuadratic forms to optimize functions. To do this: 3.1.- Knowing the normed space. 3.2.- Studying the sign of a cuadratic form in Rn and also when restricted to a subspace. 4.- Being able to compute the sum of an infinite series of real numbers. To do this: 4.1.- Knowing about sequences of real numbers and having tools to compute their limit. 4.2.- Defining series from sequences and computing their sum. 5.- Being able to study a real valued function with real variable. To do this: 5.1.- Being able to solve limits, continuity and derivability of a function. 5.2.- Knowing the procediure for graphic representation of functions.|
Ths syllabus contains two different parts.
Parte I: Linear Algebra. (Units 1-5), note that cuadratic forms are not linear.
Parte II: Single variable calculus (Temas 6 y 7)
The contents of this teaching guide have been agreed by the mathematics area and therefore are similar in every campus in the UCLM where this degree is offered.
All training activities will be recoverable, in other words, there must be an alternative evaluation test that allows to reassess the acquisition of the same skills in the ordinary, extraordinary and special call for completion. If exceptionally, the evaluation of any of the training activities cannot be recovered, it must be specified in the description and be expressly authorized by the department.
|Training Activity||Methodology||Related Competences||ECTS||Hours||As||Com||Description|
|Class Attendance (theory) [ON-SITE]||Lectures||E07 E11||1.33||33.25||N||N||Teaching the subject by lecturer (MAG)|
|Class Attendance (practical) [ON-SITE]||Problem solving and exercises||E07 E11 G01||0.67||16.75||N||N||Worked example problems and cases resolution by the lecturer and the students (PRO)|
|Other on-site activities [ON-SITE]||Assessment tests||E07 E11 G01||0.1||2.5||Y||N||Other evaluation activities (EVA)|
|Progress test [ON-SITE]||Assessment tests||E07 G01||0.1||2.5||Y||N||Test on Linear Algebra (EVA)|
|Final test [ON-SITE]||Assessment tests||E07 G01||0.1||2.5||Y||Y||Final test of the complete syllabus of the subject (EVA)|
|Other off-site activity [OFF-SITE]||Problem solving and exercises||G01||0.2||5||N||N||Self study (EST)|
|Study and Exam Preparation [OFF-SITE]||Self-study||E07 E11 G01||1.4||35||N||N||Self study (EST)|
|Group tutoring sessions [ON-SITE]||Group tutoring sessions||E07 G01||0.1||2.5||N||N||Individual or small group tutoring in lecturer's office, classroom or laboratory (TUT)|
|Other off-site activity [OFF-SITE]||Self-study||E07 G01||2||50||N||N||Self study (EST)|
|Total credits of in-class work: 2.4||Total class time hours: 60|
|Total credits of out of class work: 3.6||Total hours of out of class work: 90|
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
|Evaluation System||Continuous assessment||Non-continuous evaluation *||Description|
|Progress Tests||10.00%||0.00%||Progress Test of the Linear Algebra part.|
|Other methods of assessment||10.00%||0.00%||Non-compulsory activity that can be retaken. To be carried out before end of teaching period|
|Final test||80.00%||100.00%||Final test of the whole syllabus.|
|Not related to the syllabus/contents|
|Class Attendance (theory) [PRESENCIAL][Lectures]||33.25|
|Class Attendance (practical) [PRESENCIAL][Problem solving and exercises]||16.75|
|Other on-site activities [PRESENCIAL][Assessment tests]||2.5|
|Progress test [PRESENCIAL][Assessment tests]||2.5|
|Final test [PRESENCIAL][Assessment tests]||2.5|
|Other off-site activity [AUTÓNOMA][Problem solving and exercises]||5|
|Study and Exam Preparation [AUTÓNOMA][Self-study]||35|
|Group tutoring sessions [PRESENCIAL][Group tutoring sessions]||2.5|
|Other off-site activity [AUTÓNOMA][Self-study]||50|
|Author(s)||Title||Book/Journal||Citv||Publishing house||ISBN||Year||Description||Link||Catálogo biblioteca|
|Anton, H||Introducción al álgebra lineal||Limusa||ISBN: 978-968-18-631||2010|
|Arvesú Carballo, Jorge||Problemas resueltos de álgebra lineal||Thomson||84-9732-284-3||2005|
|Barbolla, R. y Sanz, P.||Algebra lineal y teoría de matrices||Prentice Hall||2001|
|Blanco García, S. García Pineda, P. y Pozo García, E.||Matemáticas empresariales I. Enfoque teórico y práctico. Vol. 2. Cálculo||AC Madrid||ISBN: 84-9732-172-3||2002|
|Blanco García, S.; García Pineda, P. y Pozo García, E.||Matemáticas empresariales I. Enfoque teórico y práctico. Vol I. Álgebra lineal.||AC Madrid||ISBN: 84-9732-171-5||2002|
|Burgos Román, J.||Álgebra Lineal||McGraw-Hill||ISBN: 84-481-0134-0||1997|
|Calvo, M. E. y otros||Problemas resueltos de matemáticas aplicadas a la economía y la empresa.||AC||2003|
|Cancelo, J. R., López Ortega, J. y otros.||Problemas de álgebra lineal para economistas.||Tebar Flores||1995|
|Cámara Sánchez, A.||Problemas resueltos de matemáticas para economía y empresa.||Thomson AC||ISBN: 978-84-9732-17||2007|
|García, A., García, F. y A. Gutiérrez.||Cálculo I. Teoría y Problemas de Análisis Matemático en una Variable.||Clagsa||1998|
|Gutiérrez, S.||Álgebra Lineal para la Economía.||AC||2002|
|Jarne, G. ; Perez-Grasa, I. ; Miguillón, E.||Matemáticas para la economía: álgebra lineal y cálculo diferencial.||McGraw-Hill||ISBN: 84-481-1197-4.||2004|
|López, M. y Vegas, A.||Curso básico de matemáticas para la economía y la dirección de empresas I.||Pirámide||2001|
|Stewart, J||Cálculo en una variable.||Thomson||2001|
|Sydsaeter, K.||Matemáticas para el análisis económico.||Prentice Hall||ISBN: 0-13-240615-2.||2006|
|Vignerón Tenorio A. y Beato Sirvent, J.||Matemáticas básicas para la Economía y la Empresa.||Servicio de Publicaciones de la Universidad de Cádiz||2006|