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## Syllabus 2019-20 - 11311009 - Mathematics 1 (Matemáticas I)

- Level 1: Tutorial support sessions, materials and exams in this language
- Level 2: Tutorial support sessions, materials, exams and seminars in this language
- Level 3: Tutorial support sessions, materials, exams, seminars and regular lectures in this language

DEGREE: | Grado en Finanzas y contabilidad (11311009) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

DEGREE: | Grado en Administración y dirección de empresas (11111009) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

DEGREE: | Grado en Administración y dirección de empresas (11121009) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

DEGREE: | Doble Grado en Administración y dirección de empresas y Finanzas y contabil (11911009) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

ACADEMIC YEAR: | 2019-20 |

COURSE: | Mathematics 1 |

NAME: Mathematics 1 | |||||

CODE: 11311009 (*) | ACADEMIC YEAR: 2019-20 | ||||

LANGUAGE: English | LEVEL: 3 | ||||

ECTS CREDITS: 6.0 | YEAR: 1 | SEMESTER: PC |

NAME: GUERRERO GARCIA, JULIO | ||

DEPARTMENT: U124 - MATEMÁTICAS | ||

FIELD OF STUDY: 595 - MATEMÁTICA APLICADA | ||

OFFICE NO.: B3 - B3-035 | E-MAIL: jguerrer@ujaen.es | P: 953 213375 |

WEBSITE: - | ||

ORCID: - | ||

LANGUAGE: - | LEVEL: 3 | |

NAME: LÓPEZ MORENO, ANTONIO JESÚS | ||

DEPARTMENT: U124 - MATEMÁTICAS | ||

FIELD OF STUDY: 595 - MATEMÁTICA APLICADA | ||

OFFICE NO.: B3 - 28 | E-MAIL: ajlopez@ujaen.es | P: 953212932 |

WEBSITE: www4.ujaen.es/~ajlopez | ||

ORCID: https://orcid.org/0000-0001-6701-7550 | ||

LANGUAGE: - | LEVEL: 3 |

**
Chapter
1: Functions.**
The
real line. Real functions of one variable. Main functions in
Analysis and Economy. Limits and continuity. Economic modelling by
means of functions and limits.

**
Chapter
2. Differentiation of functions.**
The
derivative, pointwise rate of change in economic modelling,
geometric interpretation. Computations of derivatives. Derivative
and shape preserving properties of a function.
L'Hôpitalâââââ€š¬Å¡¬ââââ€š¬ÂÂž¢s
theorem.

**
Chapter
3. Integration of functions.**
Primitive
of a function, indefinite integral and its properties. Computation
of primitives. Definite integral and its properties. Applications
of the definite integral.

**
Chapter
4. Matrices.**
Data
representation by means of matrices. Basic definitions and matrix
operations. Matrix power and matrix iterative models. Rank of a
matrix. Determinant. Inverse matrix.

**
Chapter
5. Systems of linear equations.**
Vectors.
Classification of systems of linear equations. Parametric
expression of the solution of a linear system. Cramer's Rule and
Gauss Elimination. Linear subspace. Basis, coordinates and
dimensión for linear subspaces.

**
Chapter
6. Matrix diagonalization.**
Diagonalization
process: eigenvalues, eigenvectors and characteristic polynomial.
Interpretation of eigenvalues and eigenvectors and tendence in
iterative matrix models.
Tendency
study in matrix models.

Classes of theory for all the group (big group): The theoretical aspects of the subjects will be exposed along with general practical examples.

Problems classes in small groups: 15 hours will be devoted to the resolution of problems and exercises with applications in Economy.

Computer classes in small groups: 15 hours will be carried out in the computer laboratory with the aid of the software Wolfram Research Mathematica.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

**
Items
considered to compute the mark:**

**
(S1)**
(1
point = 10% of the total mark) Attendance and/or participation: The
attendance to the theory, problems and computer classes will be
considered taking into account the active participation of the
students, in the terms that the professor will determine, to give
the following points:

- Theory/problems: 0.5 points (5%).
- Computer practices: 0.5 point (5%): in proportion to the number of computer sessions attended.

**
(S2)**
(8
points = 80% of the total mark) Basic concepts of the
subject.

- Theory/problems, 7 points (70%): Written exam at the end of the quarter . The professor could propose a continuous assessment system by means of which the students could obtain the 7 points corresponding to the final exam along the quarter.
- Computer practices, 1 point (10%): Exam in the computer classroom at the end of the quarter .

**
(S3)**
(1
point = 10% of the total mark) Works, exercises or short exams
proposed by the professor along the quarter.

The following criteria will also be applied:

- The points obtained in (S1) and (S3) will be maintained for all the official exam calls of the course.
- The mark obtained in the exam of computer practices, item (S2)-2, will be maintained for all the official exam calls of the course. Only the last mark obtained in an official practices exam will be considered no matter if the student had better marks in previous calls.
- The final mark of those students that did not attend the theory exam, item (S2)-1, will be "No Presentado" , no matter if they participate in any of the rest of activities of the course.
- The final mark will be sum of the points obtained in (S1), (S2) and (S3) provided that in the theory exam, (S2)-1, the student obtains more than 3 points (out of 10).
- Exceptionally and whenever it is accredited enough, the students could be evaluated taking into account items (S2)-1 and (S2)-2 only (with weight 80% and 20%, respectively).