Type A

Code 
Competences Specific   A2 
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 
Type A

Code 
Learning outcomes 
 A2 
Use integral calculation to relate magnitudes.
Use matrices to represent and work with economic, business and financial information.
Use matrices to analyze information about economic systems represented by linear equations.
Understand the multidimensional space of economic decisions.
Use functions to relate two economic and financial magnitudes.

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.
Take notes during a class.
  C2 
Use software for online communication: interactive tools (web, moodle, blogs, etc.), email, forums, chat rooms, video conferences, collaborative work tools, etc.
  C4 
Produce written texts that are appropriate to the communicative situation

Topic 
Subtopic 
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 Definitions and examples
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

Methodologies :: Tests 

Competences 
(*) Class hours

Hours outside the classroom

(**) Total hours 
Introductory activities 

1 
0 
1 
Lecture 

24 
24 
48 
Problem solving, classroom exercises 

25 
25 
50 
Problem solving, exercises 

0 
25 
25 
ICT practicals 

0 
10 
10 
Personal tuition 

4 
0 
4 

Objective shortanswer tests 

2 
2 
4 
Practical tests 

2 
2 
4 
Objective multiplechoice tests 

2 
2 
4 

(*) On elearning, 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

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. 
Description 
Time that each teacher has to speak to pupils and resolve their doubts. 
Methodologies 
Competences

Description 
Weight 




Objective shortanswer tests 

4 brief exercises about particular issues. Each exercise weights 10%; from these 4 exercises, we consider the 3 best scores. 
30% 
Practical tests 

Final exam is about all the contents of the subject. 
70% 
Objective multiplechoice tests 

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. Only scientific calculators will be allowed during evaluation activities. 
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, McGrawHill, 2007,
Vilella Bach, Cori, Apunts de Matemàtiques I, Publicacions de la Universitat Rovira i Virgili, 2011,
Mauri Masdeu, L., Matemàtiques I: Economia i empresa, Publicacions URV, 2012, Tarragona


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


Subjects that continue the syllabus 

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

