## MATHEMATICS

### Course

Code: 4167

Degree: Dual Bachelor's in Law and Business Administration and Management

Faculty of Social and Legal Sciences of Elche

Year: Year 1 of Dual Bachelor's in Law and Business Administration and Management

Semester: Fall

Type: Core

Language: Spanish

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

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 | ■ | ||

MARCOS SANMARTIN, ENCARNACION | ■ | ■ |

### Professional interest

### Competencies and learning outcomes

#### General competencies

- Ability to implement efficient tools for troubleshooting within the branch of social and legal sciences.
- Critical and analytical skills in the relevant specialty area.
- Capacity to evaluate, optimize, and compare criteria in decision making.
- 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.

#### Specific competencies

- Ability to analyze general problems within the field of microeconomics and macroeconomics.
- Capacity to perceive and value the importance of new technologies within the business environment and its economic surroundings.
- Capacity to use and interpret business data and information for specialized reporting and decision making.

#### 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.
- 09alculate 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 | U1 | 4 | 2 | 2 | 8 |

2 | U1,U2 | 4 | 2 | 2 | 8 |

3 | U2 | 4 | 2 | 5 | 11 |

4 | U2 | 4 | 2 | 4 | 10 |

5 | U2,U3 | 4 | 2 | 6 | 12 |

6 | U3 | 4 | 2 | 4 | 10 |

7 | U3 | 4 | 2 | 4 | 10 |

8 | U3 | 4 | 2 | 4 | 10 |

9 | U4 | 4 | 2 | 6 | 12 |

10 | U4 | 4 | 2 | 4 | 10 |

11 | U4,U5 | 4 | 2 | 4 | 10 |

12 | U5 | 4 | 2 | 3 | 9 |

13 | U6 | 4 | 2 | 4 | 10 |

14 | U6,U7 | 4 | 2 | 4 | 10 |

15 | U7 | 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.
- Caballero Fernández, Rafael E. "Matemáticas aplicadas a la economía y a la empresa 434 ejercicios resueltos y comentados". Madrid Pirámide D.L.2000.
- 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].
- 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.

#### Complementary bibliography

- 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.
- 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.
- Burgos Román, Juan de. "Cálculo infinitesimal de una variable". Madrid McGraw-Hill, Interamericana de España 19941997.
- Burgos Román, Juan de. "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.

#### 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.