Guías Docentes Electrónicas
1. General information
ECTS credits:
Academic year:
First quarter
Main language:
Second language:
Use of additional languages:
English Friendly:
Web site:
Lecturer: ALVARO MARTINEZ PEREZ - Group(s): 60 
Phone number
Office hours
Despacho 2.9
First semester: Tuesdays from 9 to 11 and from 16 to 18. Fridays from 9 to 11 and from 14 to 15. Second semester: Thursday from 9:30 to 11:30 and from 16 to 18 and Fridays from 9 to 11 and from 15 to 17.

2. Pre-Requisites

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.

3. Justification in the curriculum, relation to other subjects and to the profession

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. 

4. Degree competences achieved in this course
Course competences
Code Description
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.
5. Objectives or Learning Outcomes
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.
Additional outcomes
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.
6. Units / Contents
  • Unit 1: Basic elements of linear algebra
  • Unit 2: Rn vectorial space
  • Unit 3: Linear maps and associated matrices
  • Unit 4: Matrix diagonalization
  • Unit 5: Cuadratic forms
  • Unit 6: Real numbers: sequences and series
  • Unit 7: Real valued functions of a real variable

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.

7. Activities, Units/Modules and Methodology

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: 6 150
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).

8. Evaluation criteria and Grading System
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.
Total: 100.00% 100.00%  
According to art. 6 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 13.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).

Evaluation criteria for the final exam:
  • Continuous assessment:
    Final test: The final test includes all the lessons in the syllabus (lessons 1 to 7: Linear Algebra and Single vairable Calculus) and gives a maximum of 8 points to the final grade whenever a minimum of 40% is achieved.

    Progress test: this evaluation activity on Linear Algebra gives a maximum of 1 point to the final grade of the course.

    Other evaluation activities: These self-evaluations or cooperative activities or case resoluctions, etc give a maximum of 1 point to the final grade of the course.

    Note: In case that the final exam score is less than a 40%, the continous evaluation will not be considered and the final grade of the course will be the grade of the final exam.

    Aditional note: The rules of the Mathematics Area for the realization of any exam (partial, ordinary or extrarodinary) are the following: it is forbiden to carry and/or use any cell phone (or calculator) during the exam. In case a student carries and/or uses a cell phone (or calculator) during the exam, will immediately fail with a 0 score in base of Article 9 of the Student Evaluation Regulations.
  • Non-continuous evaluation:
    The final exam will consist of the necessary tests (written or oral) to validate the competencies on the subject.

Specifications for the resit/retake exam:
Final retake exam: it will be a test including the whole syllabus (lessons 1 to 7: Linear Algebra and Single Variable Calculus) for all students and it will give a masimum of 9 points to the final grade for those whe reach at least a

Progress test: it is recovered in the final retake exam.

Other evaluation activities: these self-evaluations or cooperative activities or case resoluctions, etc keep the score in the extraordinary convocatory.

Note: As in the ordinary convocatory, if the final exam score is less than a 40%, the continous evaluation will not be considered and the final grade of the course will be the grade of the final exam.
Specifications for the second resit / retake exam:
It will be a final test which gives the 100% of the final grade.

Note: The rules of the Mathematics Area for the realization of any exam (partial, ordinary or extrarodinary) are the following: it is forbiden to carry and/or use any cell phone (or calculator) during the exam. In case a student carries and/or uses a cell phone (or calculator) during the exam, will immediately fail with a 0 score in base of Article 9 of the Student Evaluation Regulations.
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours
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

Global activity
Activities hours
10. Bibliography and Sources
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 Ficha de la biblioteca
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  

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