Educational guide
IDENTIFYING DATA 2022_23
Subject MATHEMATICS APPLIED TO BUSINESS Code 00512005
Study programme
0512 - GRADO EN COMERCIO INTERNACIONAL
Descriptors Credit. Type Year Period
6 Basic Training First First
Language
Castellano
Ingles
Prerequisites
Department MATEMATICAS
Coordinador
FERNANDEZ SUAREZ , LEONARDO
E-mail lfers@unileon.es
asuac@unileon.es
Lecturers
FERNANDEZ SUAREZ , LEONARDO
SUAREZ CORONA , ADRIANA
Web http://
General description This course in addition to providing basic mathematical knowledge to the student, how the use of mathematical reasoning. Is a tool that allow the correct use of quantitative methods that arise in different subjects of the degree as Statistics, Macroeconomics, Microecnomics...
Tribunales de Revisión
Tribunal titular
Cargo Departamento Profesor
Presidente MATEMATICAS CARRIEGOS VIEIRA , MIGUEL
Secretario MATEMATICAS TROBAJO DE LAS MATAS , MARIA TERESA
Vocal MATEMATICAS PISABARRO MANTECA , MARIA JESUS
Tribunal suplente
Cargo Departamento Profesor
Presidente MATEMATICAS GOMEZ PEREZ , JAVIER
Secretario MATEMATICAS MAZCUñAN NAVARRO , EVA MARIA
Vocal MATEMATICAS RODRIGUEZ SANCHEZ , CRISTINA

Competencias
Code  
A6386
A6456
A6457
A6458
A6473
A6477
A6501
A6536
A6578
A6579
A6601

Learning aims
Competences
A6601
A6578
A6536
A6456
A6501
A6473
A6477
A6579
A6458
A6457
A6386
A6601

Contents
Topic Sub-topic
Block A: Differential Calculus 1.-LIMITS AND CONTINUITY OF REAL FUNCTIONS
1.1 Real functions.
1.2 Functions algebra. Inverse function.
1.3 Limit of a function at a point. Properties of limits.
1.4 Equivalent functions. Infinites and infinitesimals
1.5 Continuity of a function at a point. Discontinuities.
1.6 Properties of continuous functions.


2.- DERIVABILITY OF REAL FUNCTIONS
2.1 Derivative of a function at a point. Interpretations.
2.2 Derivative computations.
2.3 Continuity and derivability.
2.4 Properties of differentiable functions
2.5 Higher order derivatives
2.6 Implicit differentiation.



3.- PROPERTIES AND APPLICATIONS OF THE DERIVATIVE OF A FUNCTION.
3.1 Theorems of differentiable functions. L'Hopital rule.
3.2 Taylor polynomial.
3.3 Relative and absolute extrema.
3.4 Necessary and sufficient conditions for the existence of extrema.
3.5 Concavity y convexity. Inflection points
3.6 Aplications of the derivative to Economy.
Block B: Integral Calculus TEMA 4.- INTEGRATION
4.1 Definite integral: concept.
4.2 Properties of the definite integral.
4.3 Fundamental Theorem of Calculus. Barrow's rule
4.4 Improper integrals
4.5 Primitive functions. Integration methods.
4.6 Applications of the integral to Economy.
Block C: Linear algebra 5.- SYSTEMS OF LINEAR EQUATIONS
5.1 Concept and how to solve systems of linear equations.
5.2 Types of systems. Equivalent systems.
5.3 Gaussian elimination.

6.- MATRICES
6.1 Definition of matrix. Types.
6.2 Matrix algebra. Properties.
6.3 Matrices and systems of linear equations. Rank of a matrix
6.4 Inverse of a matrix.
6.5 Applications of matrices.

Planning
Methodologies  ::  Tests
  Class hours Hours outside the classroom Total hours
Lecture 20 30 50
 
Problem solving, classroom exercises 14 25.2 39.2
Practicals using information and communication technologies (ICTs) in computer rooms 6 10.8 16.8
 
Personal tuition 9 4 13
 
Practical tests 6 11 17
Extended-answer tests 5 9 14
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies   ::  
  Description
Lecture
Problem solving, classroom exercises
Practicals using information and communication technologies (ICTs) in computer rooms
Personal tuition

Personalized attention
 
Problem solving, classroom exercises
Lecture
Practical tests
Extended-answer tests
Description
In class or at the professor office, by appointment. Also by email, the Moodle forum or through a videoconference platform.

Assessment
  Description Qualification
Problem solving, classroom exercises 5%
Lecture 5%
Practical tests 20%
Extended-answer tests 70%
 
Other comments and second call

 

1. Language
There will be lectures both in English and Spanish. Most part of the material will be written in English. The tests and office hours can be done in both languages. 
2. Course character.

The course will be mainly practical, where the theoretical concepts will be applied. The student, however, has to understand all the theoretical concepts to be able to apply them and solve and interpret the solutions of the practical problems.  

3. Recommendations for autonomous learning.

For the autonomous learning of the student, it is recommended: 

- The bibliography  of the course and the lecture notes are essential to study. 

- Before the lectures, it is recommended that the student works with the material to foster their active participation in class both in theoretical lectures and try to solve the problems and practical assignments before problem and software sessions. 

 

4. Assessment.

There will be continuous assessment. The student will pass the course if he/she scores at least 5 out of 10 points.

To this aim, the professor will take into account the continuous work of the students and their results in the tests and practical exams, to see how the competences are acquired by the student. 

In particular, the assessment takes into account:

  1. Two midterm exams. Each test accounts for 35% of the total grade. If a test is passed, the content of this test won't be directly present in the other test. 
  2. Practical exams, which accounts for 20% of the grade. 
  3. Participation, positive attitude and assignment performance in theoretical lectures, practical and problem sessions, seminars and office hours, can account up to 10%. 

During the tests the student is not allowed to use any material, unless the professor explicitly allows it. It is forbidden to use cell phones or any other electronic devices while doing the tests. If a student has notes, books or any other material or device not allowed during the tests, the student will not be able to finish the test and will be expelled from the test and will not pass the exam. Moreover, the Academic Authorities will be informed, so that the normative on Plagiarism and Fraud can be applied.  

5. Second call.

Those students not passing the course on the first call, will be able to retake the tests they haven't passed, keeping the grades of the passed tests. 

To pass the course in the second call the student needs to score at least 5 out of 10 points. 

6. December call.

 For the students about to finish the degree (only the Degree Thesis and a course has not been passed), can take the exam in the December call, which will consist on a test and the student will need to score at least 5 out of 10 points. 

 

 

Sources of information
Access to Recommended Bibliography in the Catalog ULE

Basic PÉREZ-GRASA I. Y OTROS, Matemáticas para la Economía. ProgramaciónMatemática y Sistemas Dinámicos , McGraw-Hill, 2001 ,
BURGOS, J., Algebra lineal, McGraw-Hill, 2000,
LARSON, R., HOSTETLER, R., Cálculo (volumen I), McGraw-Hill. 2008,
GARCÍA, A. Y OTROS, Cálculo I, CLAGSA, 1993 ,
BURGOS, J., Cálculo infinitesimal de una variable, McGraw-Hill ,1994,
COQUILLAT, F., Cálculo Integral. Metodología y problemas, Tebar Flores, 1997 ,
, http://www.economicas.unileon.es, , Web de la Facultad
, https://agora.unileon.es/login/index.php, , Plataforma Moodle
ANTON H., TORRES CH. , Introducción al Álgebra lineal, Limusa. México, 1994,
SAMAMED, O. Y OTROS, Matemáticas I. Economía y Empresa. Problemas resueltos, C.E.R.A. ,1995 ,
SAMAMED, O. Y OTROS, Matemáticas I. Economía y Empresa. Teoría., C.E.R.A., 1998,
SYDSAETER, K., HAMMOND PETER J. , Matemáticas para el análisis económico, Pearson, Prentice Hall, 2010,
MINGUILLÓN E. Y OTROS, Matemáticas para la Economía. Libro de ejercicios. Algebra Lineal y Cálculo Diferencial, McGraw-Hill, 2004,
CABALLERO, Rafael y otros, Métodos Matemáticos para la Economía , McGraw-Hill, 1992,
DE DIEGO MARTIN, B., Problemas de algebra lineal, Deimos, 1995 ,
TEBAR FLORES, E., Problemas de cálculo infinitesimal, Tebar Flores, 2005 ,

Complementary GALINDO SOTO, F. SANZ GIL, J. TRISTAN VEGA, Guía práctica de cálculo infinitesimal en una variable, Thomson, 2003 ,
, http://www.britannica.com/, , Enciclopedia
, http://www.calculator.com/calcs/calc_sci.html, , Calculadora
, http://www.terra.es/personal/agmh25/genios/home.htm, , Grandes Matemáticos


Recommendations


 
Other comments
It is recommended that the students have taken mathematics at "Segundo de Bachillerato" level and have at least a B2 level in English.