IDENTIFYING DATA 2012_13
Subject (*) MATHEMATICS I Code 16224008
Study programme
Degree of Economics (2009)
Cycle 1st
Descriptors Credits Type Year Period
6 Basic Course First First
Language
Anglès
Català
Department Gestió d'Empreses
Coordinator
FERNÁNDEZ BARIVIERA, AURELIO
MARQUEZ ALVAREZ, NORBERTO
VILELLA BACH, MISERICÒRDIA
LLERENA GARRÉS, FRANCISCO
E-mail norberto.marquez@urv.cat
francisco.llerena@urv.cat
cori.vilella@urv.cat
aurelio.fernandez@urv.cat
llucia.mauri@urv.cat
cristina.tomas@urv.cat
Lecturers
MARQUEZ ALVAREZ, NORBERTO
LLERENA GARRÉS, FRANCISCO
VILELLA BACH, MISERICÒRDIA
FERNÁNDEZ BARIVIERA, AURELIO
MAURI MASDEU, LLUCIA
TOMÁS MONTERDE, CRISTINA
Web http://moodle.urv.cat
Relevant information Desenvolupament de les eines algebraiques i d'anàlisi real necessàries per a l'ensenyament.

Competences
Type A Code Competences Specific
 A2 Students master the basic methods and tools for analyzing business reality.
 A3 Students can find, analyze and interpret quantitative and qualitative information of a financial, accounting, economic, social and legal nature that is relevant to the taking of business decisions.
Type B Code Competences Transversal
 B2 Effective solutions to complex problems
Type C Code Competences Nuclear
 C1 Have an intermediate mastery of a foreign language, preferably English
 C2 Be advanced users of the information and communication technologies
 C4 Be able to express themselves correctly both orally and in writing in one of the two official languages of the URV

Learning outcomes
Type A Code Learning outcomes
 A2 Relaciona dues magnituds econòmico-financeres mitjançant funcions.
 A3 Utilitza eines de càlcul integral per relacionar magnituds.
Representa i opera matricialment la informació quantitativa de caràcter econòmic, empresarial i financer.
Analitza matricialment la informació dels sistemes econòmics representats per sistemes d'equacions lineals.
Entén l'espai de decisions econòmiques multidimensional.
Type B Code Learning outcomes
 B2 Collect the information they need so that they can solve problems using data and not subjective opinion, and subjecting the information at their disposal to logical analysis.
Find appropriate solutions.
Type C Code Learning outcomes
 C1 Understand instructions about classes or tasks assigned by the teaching staff.
Recollir en apunts part de la informació que s'imparteix en una classe
 C2 Use software for on-line communication: interactive tools (web, moodle, blogs, etc.), e-mail, forums, chat rooms, video conferences, collaborative work tools, etc.
 C4 Produce written texts that are appropriate to the communicative situation

Contents
Topic Sub-topic
PART I: LINEAR ALGEBRA 1. Matrices and determinants
1.1 Matrix operations
1.2 Determinant of a matrix
1.3 Rank of a matrix

2. Systems of linear equations
2.1 Definition of a system of linear equations
2.2 Classification of systems
2.3 Resolution of systems

3. The vector space Rn
3.1 Operations on vectors
3.2 Linear dependence and linear independence
3.3 Scalar product
PART II: REAL ANALYSIS 4. Real functions of one real variable
4.1 Continuous functions. Classes of discontinuous functions
4.2 Derivative and elasticity of a function
4.3 Local and global extrema. Increasing and decreasing functions
4.4 Concavity and convexity
4.5 Graphical representation of functions

5. Integration
5.1 Indefinite integral
5.2 Definite integral

Planning
Methodologies  ::  Tests
  Competences (*) Class hours
Hours outside the classroom
(**) Total hours
Introductory activities
C1
C4
1 0 1
Lecture
A2
A3
B2
C1
C4
24 24 48
Problem solving, classroom exercises
A2
A3
B2
C1
C4
25 25 50
Problem solving, exercises
A2
A3
B2
C1
C4
0 25 25
ICT practicals
A2
A3
B2
C1
C2
C4
0 10 10
Personal tuition
B2
4 0 4
 
Objective short-answer tests
A2
A3
B2
C1
C4
2 2 4
Practical tests
A2
A3
B2
C1
C4
2 2 4
Objective multiple-choice tests
A2
A3
B2
C1
C2
2 2 4
 
(*) On e-learning, hours of virtual attendance of the teacher.
(**) The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies
  Description
Introductory activities Activities designed to make contact with students, collect information from them and introduce the subject.
Lecture Description of the contents of the subject.
Problem solving, classroom exercises Formulation, analysis, resolution and debate of a problem or exercise related to the topic of the subject.
Problem solving, exercises Formulation, analysis, resolution and debate of a problem or exercise related to the topic of the subject.
ICT practicals Practical application of the theory of a knowledge area in a particular context. Practical exercises using ICTs.
Personal tuition Temps que cada professor té reservat per atendre i resoldre dubtes als alumnes.

Personalized attention
Description
Time that each teacher has to speak to pupils and resolve their doubts.

Assessment
Methodologies Competences Description Weight        
Objective short-answer tests
A2
A3
B2
C1
C4
4 brief exercises about particular issues. Each exercise weights 10%; from these 4 exercises, we considerate the 3 best scores. 30%
Practical tests
A2
A3
B2
C1
C4
Final exam is about all the contents of the subject. 70%
Objective multiple-choice tests
A2
A3
B2
C1
C2
Proves d'autoavaluació 0%
Others  
 
Other comments and second call

The 100% of second examination session is a final exam about all the contents of the subject.


Sources of information

Basic Sydsaeter, K., Hammond, P., Mathematics for economic analysis, Prentice Hall, 1995,
Sanz, P. et al, Problemas de álgebra lineal. Cuestiones ejercicios y tratamiento en Derive, Prentice Hall, 1998, Madrid
Hammond, P., Sydsaeter, K., Matemáticas para el análisis económico, Prentice Hall, 1996, Madrid
Alegre, P. et al, Ejercicios resueltos de matemáticas empresariales, Vol I, AC, 1991, Madrid
Hoffmann, L. D., Bradley, G. L., Applied calculus: for business, economics, and the social and life sciences, McGraw-Hill, 2007,

Complementary Hoffmann, L. D. et al., Cáculo aplicado a la administración, economía, contaduría y ciencias sociales, McGraw-Hill, 1994, Santafé de Bogotá
Alejandre, F. et al, Problemes de matemàtiques per econòmiques i empresarials, Media, 1995, Sant Cugat del Vallès

Recommendations

Subjects that continue the syllabus
MATHEMATICS II/16204009

Subjects that are recommended to be taken simultaneously
INTRODUCTION TO MICROECONOMICS/16204004

(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.