## MATHEMATICS

### Course

Code: 1183

Degree: Bachelor's in Business Statistics

Faculty of Social and Legal Sciences of Elche

Year: Year 1 of Bachelor's in Business Statistics

Semester: Fall

Type: Core

Language: Spanish

ECTS credits: 6 Lecture: 3 Laboratory: 3 | Hours: 150 Directed: 60 Shared: 30 Autonomous: 60 |

Subject matter: Mathematics

Module: Mathematics

Department: Statistics, Mathematics and Informatics

Area: APPLIED MATHEMATICS

Course instructors are responsible for the course content descriptions in English.

### Description

### Faculty

Name | Coordinator | Lecture | Laboratory |
---|---|---|---|

HERRANZ CUADRADO, MARIA VICTORIA | ■ | ■ | ■ |

SANCHEZ MARTINEZ, JOSE RAFAEL | ■ |

### Professional interest

### Competencies and learning outcomes

#### General competencies

- Capacity to identify, interpret, formulate, and resolve basic problems within the field of social and legal sciences.
- Capacity for planning, organizing, directing, and controlling systems and processes within a framework that guarantees respect for the values, rights and basic principles of the legal system, business competitiveness, protection and conservation of the environment, and sustainable development in the corresponding field.
- Ability to implement efficient tools for troubleshooting within the field of social and legal sciences.
- Ability to communicate in formal, graphic, and symbolic styles, as well as with oral and written forms of expression.
- Ability to work with multidisciplinary and multicultural teams.
- Disposition for methodologies and efficient self-learning skills to adapt to and update new knowledge and scientific advances, as well as to changing needs in order to adopt an aptitude for innovation and creativity in the profession.

#### Specific competencies

- Ability to develop the mathematical tools necessary for resolving problems that arise in the statistical analysis of data.
- Skills for analytically and computationally resolving mathematical problems that arise in the statistical analysis of data.
- Ability to correctly and rationally use software in the analysis of data for decision making.
- Ability to think and reason quantitatively.
- Capacity for abstraction.
- Acquire the basic training for conducting research activities.

#### Objectives (Learning outcomes)

- 01Acquire and use mathematical language fluently, both orally and in writing, and rigorous formalization and structuring of a real problem in the form of mathematical problem.
- 02Ability to apply knowledge, methods and algorithms to situations and problems in the area of economic enterprise.
- 03Correctly handle the literature and information sources available to strengthen and expand knowledge and increase torque capacity to pose and solve mathematical so many problems that may arise and relate to the subject.
- 04Use various technological tools (such as computer software) that facilitate solving math problems and understand the limitations of such tools.
- 05Knowledge and skill in handling major real functions of real variable linear, quadratic, polynomial, rational, trigonometric, exponential, logarithmic. Being able to use them as a tool to solve a large variety of problems.
- 06Calculate domains and limits of functions of one and several variables. Understand and interpret the concept of continuity of functions of one or several variables.
- 07Correctly interpret graphic representations of functions and their level curves.
- 08Understand the concept of derivative of a function and its economic interpretation.
- 09Calculate derivatives of functions of several variables, both first order and higher orders. Use them to solve optimization problems.
- 010To know how to compose functions and derive composite functions by chain rule.
- 011Recognize homogeneous functions and calculate the degree of homogeneity.
- 012Master and internalize integration as the reverse process of differentiation. Know how to calculate actual primitive functions through the application of different methods of integration. Apply the concept of definite integral to determine areas.
- 013Know the theory of matrices and determinants, matrix operations and dominate the calculation of determinants. Apply the matrix calculus to the discussion and resolution of systems of linear equations. Get the inverse of a matrix.
- 014Internalize the concept of vectorial subspace, as well as to know how to obtain the parametric and implicit equations and a basis of the subspace.

### Contents

#### Teaching units

#### Association between objectives and units

Objective/Unit | U1 | U2 | U3 | U4 | U5 | U6 | U7 |
---|---|---|---|---|---|---|---|

01 | |||||||

02 | |||||||

03 | |||||||

04 | |||||||

05 | |||||||

06 | |||||||

07 | |||||||

08 | |||||||

09 | |||||||

010 | |||||||

011 | |||||||

012 | |||||||

013 | |||||||

014 |

#### Schedule

Week | Teaching units | Directed hours | Shared hours | Autonomous hours | Total hours |
---|---|---|---|---|---|

1 | 4 | 2 | 2 | 8 | |

2 | 4 | 2 | 2 | 8 | |

3 | 4 | 2 | 5 | 11 | |

4 | 4 | 2 | 4 | 10 | |

5 | 4 | 2 | 6 | 12 | |

6 | 4 | 2 | 4 | 10 | |

7 | 4 | 2 | 4 | 10 | |

8 | 4 | 2 | 4 | 10 | |

9 | 4 | 2 | 4 | 10 | |

10 | 4 | 2 | 6 | 12 | |

11 | 4 | 2 | 4 | 10 | |

12 | 4 | 2 | 3 | 9 | |

13 | 4 | 2 | 4 | 10 | |

14 | 4 | 2 | 4 | 10 | |

15 | 4 | 2 | 4 | 10 |

#### Basic bibliography

- Alejandre Chavero, Manuel J. Cañavate Bernal, Roberto J. / Herraz Cuadrado, María Victoria. "999 Problemas de análisis matemático". Elche Universidad Miguel Hernández 1999.
- Larson, Roland E. Hostetler, Robert P. "Cálculo y geometría analítica". Madrid, [etc.] McGraw-Hill D.L. 1994.
- Marsden, Jerrold Eldon. Tromba, Anthony J. "Cálculo vectorial". México Addison Wesley Longman 1998.
- Burgos, Juan de (Burgos Román). "Cálculo infinitesimal (Teoría y problemas)". Madrid Alhambra 1984.
- Caballero Fernández, Rafael E. "Matemáticas aplicadas a la economía y a la empresa 434 ejercicios resueltos y comentados". Madrid Pirámide D.L.2000.
- Strang, Gilbert. López Mateos, Manuel / Meza, Margarita de. "Álgebra lineal y sus aplicaciones". Argentina [etc.] Addison-Wesley Iberoamericana cop. 1986.
- García López, Alfonsa. "Cálculo I Teoría y problemas de análisis matemático en una variable". Madrid CLAGSA D.L. 1998.
- García López, Alfonsa. "Cálculo II Teoría y problemas de funciones de varias variables". [Madrid] Clagsa [1996].

#### Complementary bibliography

- Burgos, Juan de (Burgos Román). "Cálculo infinitesimal de una variable". Madrid McGraw-Hill, Interamericana de España 19941997.
- Burgos, Juan de (Burgos Román). "Cálculo infinitesimal de varias variables". Madrid[etc.] McGraw-Hill D.L. 1995.
- Tébar Flores, E. "Problemas de álgebra lineal". Madrid [etc.] Tebar Flores D.L. 1977.
- Bru, Rafael. "Problemas de álgebra lineal". Valencia Universidad Politécnica de Valencia, Servicio de Publicaciones [1998].
- Alejandre Chavero, Manuel J. Soler i Escriváa, Xaro / Toledo Melero, Fco. Javier. "Problemas de matemáticas asistidos con DERIVE 5 Análisis matemático". Elx Universidad Miguel Hernández 2002.
- Alejandre Chavero, Manuel J. Soler i Escriváa, Xaro / Toledo Melero, Fco. Javier. "Problemas de matemáticas asistidos con DERIVE 5 Álgebra lineal". Elx Universidad Miguel Hernández 2002.
- Amigó García, José María. "Fundamentos de Matemáticas". Elche Universidad Mihuel Hernández D.l. 2000.

#### Links

#### Software

- DERIVE 6

### Methodology and grading

#### Methodology

**Lecture:**Pass on knowledge and activate cognitive processes in students, encouraging their participation.**Problem-based learning:**Develop active learning strategies through problem solving that promote thinking, experimentation, and decision making in the student.**Solving exercises and problems:**Exercise, test, and apply previous knowledge through routine repetition.

#### Grading

In February the student will be able to choose between a system of continuous evaluation system or a final evaluation system.

**Continuous evaluation system:**

The final grade will be obtained as follows:

FINAL MARK = 0.85xE + 0.1xP + 0.05xT, where

E = final exam mark (0-10)

P = computer exam mark (0-10)

T = The assistance at the problems workshops and / or participation in the class , seminars, tutorials, etc. punctuation for tutorials (0-10). The number of participations and the quality of them will be valued fundamentally.

To pass the course it will be necessary to obtain E with a mark of at least 4 points out of 10 and, in addition, obtain a FINAL NOTE equal to or greater than 5 points (out of 10). Those who do not meet both requirements, can take a single exam (in which the three blocks will be evaluated) on the day set for the February ordinary exam.DESCRIPTION AND QUALIFICATION OF EXAMINATIONS:

The exams will be based on the resolution of problems and issues related to the contents of the subject. The score of each exam will be about 10 points. The subject consists of three blocks of differentiated content, so the final exam will consist of three parts, one for each block, with different weights. Each block of contents is composed of the following didactic units:

1. BLOCK 1: Didactic Units 1 and 2. (30% of the E mark).

2. BLOCK 2: Didactic units 3 and 4. (40% of the E mark).

3. BLOCK 3: Didactic Units 5, 6 and 7. (30% of the E mark).Therefore, E is calculated as follows:

If the test scores of each of the blocks are equal to or greater than 4 points out of 10:E = 0.3 x Exam Mark Block 1 + 0.4 x Exam Mark Block 2+ 0.3 x Exam Mark Block 3

If any of the test scores of the blocks is less than 4 points out of 10:

E = Minimum {Exam Mark Block 1, Exam Mark Block 2, Exam Mark Block 3}DESCRIPTION AND QUALIFICATION OF PRACTICES:

There will be an exam in the last practice session, in the computer classroom. It will consist in the resolution of problems through the DERIVE program.**Final evaluation system:**

The final gmark will be obtained as follows: FINAL NOTE = 0.85xE + 0.1xP + 0.05T, where

E = final mark of a single exam (0-10), which will be held on the day set for the ordinary February session.

P = qualification of the exam of computer practices (0-10), which will be carried out after the development exam, on the day set for the ordinary call of February.

T = punctuation for tutorials, participation and attendance to class, workshops and to the activities that are programmed (0-10).

To pass the subject, it is necessary to have a FINAL MARK equal to or greater than 5 (out of 10).For the September and December exams, the mark is obtained by FINAL MARK = 0.9xE + 0.1xP, where E is the qualification obtained in the examination carried out in the corresponding call and P corresponds to the qualification of the exam of practices.

#### Correction criteria

Each problem or issue of both the development exams and the corresponding to practices, will be scored according to the quality of its approach and numerical resolution.